Direct Answer
The perpetuity growth method calculates a DCF's terminal value by assuming cash flows grow at one constant rate forever after the forecast period: Terminal Value = Final Year Cash Flow × (1 + g) / (r − g), where g is the perpetual growth rate and r is the discount rate. Analysts commonly cap g near long-run GDP or inflation expectations, since assuming a company outgrows the overall economy forever is generally considered unrealistic.
Key Takeaways
- The perpetuity growth method (also called the Gordon growth terminal value approach) converts an infinite stream of future cash flows into one present-day number.
- The formula is Terminal Value = Final Year Cash Flow × (1 + g) / (r − g).
- The growth rate g is commonly capped near long-run GDP or inflation expectations rather than a company's historical growth rate.
- Terminal value typically represents a large share of a DCF's total estimated value, so small changes in g or r can move the result substantially.
- The math breaks down if g meets or exceeds r, since the denominator (r − g) must stay positive.
What Is the Perpetuity Growth Method?
A discounted cash flow (DCF) model typically forecasts a company's cash flows explicitly for a handful of years, often five to ten, and then needs a way to account for every year of cash flow beyond that window. The perpetuity growth method handles that "everything after the forecast period" problem by assuming cash flows keep growing at one constant, modest rate forever.
That single assumption lets the infinite stream of future cash flows collapse into one number, called terminal value, calculated as of the end of the explicit forecast period. Because a DCF's total value is the sum of the discounted explicit-period cash flows plus the discounted terminal value, and because terminal value often accounts for a large share of that total, the growth rate assumption behind it carries real weight in the final valuation.
This method is one of two commonly used ways to estimate terminal value; the other, the exit multiple method, instead applies a market-based multiple (such as EV/EBITDA) to a projected final-year metric. Analysts sometimes calculate both and compare the results as a sanity check on their assumptions.
How Is Terminal Value Calculated?
The perpetuity growth method uses the following formula:
Terminal Value = Final Year Cash Flow × (1 + g) / (r − g)
- Final Year Cash Flow, the projected cash flow in the last year of the explicit forecast period.
- g, the perpetual growth rate assumed for every year after the forecast period, applied forever.
- r, the discount rate (often the weighted average cost of capital) used to bring future cash flows to present value.
Multiplying the final year's cash flow by (1 + g) produces the first year of the perpetuity, the cash flow one year beyond the forecast period, before dividing by (r − g) to capitalize that growing stream into a single value. The resulting terminal value is stated as of the end of the forecast period, so it still needs to be discounted back to the present using the same discount factor applied to the rest of the model's cash flows.
The denominator only makes sense when r is greater than g. If g is set equal to or above r, the formula produces an undefined or negative result, which is a signal the growth assumption is too aggressive relative to the discount rate being used.
Worked Example
Hypothetical example, for education only.
Suppose a five-year DCF projects a company's final year (Year 5) free cash flow at $50 million. The analyst sets a discount rate (r) of 9% and a perpetual growth rate (g) of 2.5%, roughly in line with long-run nominal GDP expectations.
| Input | Value |
|---|---|
| Final Year (Year 5) Cash Flow | $50.0M |
| Perpetual growth rate (g) | 2.5% |
| Discount rate (r) | 9.0% |
Applying the formula:
Terminal Value = $50.0M × (1 + 0.025) / (0.09 − 0.025) = $51.25M / 0.065 ≈ $788.5M
That $788.5 million figure is the terminal value as of the end of Year 5. Like the explicit forecast-period cash flows, it still has to be discounted back to today's dollars at the same 9% discount rate over five years, which brings it down to roughly $512.4 million in present value, before adding it to the present value of Years 1 through 5's cash flows to arrive at the DCF's total estimated value.
How Sensitive Is Terminal Value to the Growth Rate?
Because g sits in the denominator, small changes in the assumed growth rate can move terminal value considerably. Using the same $50 million final-year cash flow and 9% discount rate from the example above:
| Growth rate (g) | Terminal Value |
|---|---|
| 1.5% | ≈ $676.7M |
| 2.5% | ≈ $788.5M |
| 3.5% | ≈ $940.9M |
Moving g from 1.5% to 3.5%, a two-percentage-point swing well within the range analysts might reasonably debate, changes terminal value by roughly 39% in this example. That sensitivity is a core reason the growth rate is commonly capped near long-run GDP or inflation expectations rather than left to a more optimistic, company-specific figure.
How the Perpetuity Growth Method Is Used
Analysts use the perpetuity growth method as one building block inside a larger DCF, not as a standalone valuation tool. Once terminal value is calculated and discounted to the present. It is added to the present value of the explicit forecast-period cash flows to produce an estimate of enterprise value, which can then be adjusted for debt, cash, and other items to estimate equity value.
Because the method rests on a single long-run growth assumption. It is commonly used alongside the exit multiple method as a cross-check, if the two approaches produce meaningfully different terminal values, that gap can prompt a second look at the assumptions behind each. The output should be treated as a modeled estimate that depends heavily on the inputs chosen, not a precise or guaranteed figure, and different analysts modeling the same company can reasonably arrive at different results.
Limitations and Common Mistakes
- Setting g too close to r. As g approaches r, terminal value grows disproportionately large and can dominate the entire DCF output, making the model's conclusion mostly a reflection of one growth assumption.
- Using a growth rate above the long-run economy. A perpetual growth rate meaningfully above long-run GDP or inflation expectations implies a company eventually becomes larger than the entire economy, which is generally considered an unrealistic assumption.
- Mismatching the final-year cash flow to a normalized level. If the last explicit forecast year includes a one-off spike or dip, applying perpetual growth to that unusual figure carries the distortion forward indefinitely.
- Forgetting to discount terminal value back to the present. The formula's output is a value as of the end of the forecast period; it must still be discounted like any other future cash flow before being added into the DCF total.
- Treating the output as precise. Because terminal value is highly sensitive to small changes in g and r, the result is best understood as a modeled estimate, not an exact figure, a point worth stress-testing with a sensitivity table like the one above.
Frequently Asked Questions
What is the perpetuity growth method in a DCF?
The perpetuity growth method is a way to calculate terminal value in a discounted cash flow (DCF) model by assuming cash flows grow at a constant rate forever after the explicit forecast period ends. It converts an infinite stream of future cash flows into a single present-day figure using the formula Terminal Value = Final Year Cash Flow × (1 + g) / (r − g).
What is the formula for terminal value using the perpetuity growth method?
Terminal Value = Final Year Cash Flow × (1 + g) / (r − g), where g is the assumed perpetual growth rate and r is the discount rate applied to the cash flows. The resulting terminal value is then discounted back to the present using the same discount rate applied to the rest of the forecast period.
How do you choose the perpetual growth rate?
The chosen growth rate is commonly capped near long-run GDP or inflation expectations, since assuming a company grows faster than the overall economy forever is generally considered unrealistic. Analysts often use a rate in the low single digits, and the exact figure varies by analyst and by the macroeconomic assumptions built into the model.
Why can't the growth rate exceed the discount rate?
If g is greater than or equal to r, the denominator (r − g) in the terminal value formula becomes zero or negative, which produces a nonsensical or infinite result. The formula only works mathematically, and only makes economic sense, when the discount rate is higher than the assumed perpetual growth rate.
Is the perpetuity growth method reliable for valuing a company?
The perpetuity growth method is a widely used simplification, not a guarantee of a company's true value. Because terminal value often makes up a large share of a DCF's total output, small changes in the growth rate or discount rate can shift the result substantially, so most analysts treat the output as one input among several rather than a precise, final answer.
What upper bound should the perpetual growth rate respect?
A rate above long-run economic growth implies the company eventually becomes larger than the economy, which is why practitioners cap it near a long-run nominal growth estimate. Rates above that are not conservative assumptions being stretched; they are logically inconsistent. The cap is a structural constraint rather than a matter of preference.
How should the terminal cash flow be defined?
It should represent a sustainable level consistent with the assumed growth, which means the reinvestment implied by that growth must be deducted. A terminal cash flow assuming continued growth with no corresponding reinvestment overstates the perpetuity substantially. Checking the implied reinvestment against the growth rate and a plausible return on capital is the standard test.
Why is this method sensitive to small input changes?
The formula divides by the difference between the discount rate and the growth rate, so as the two converge the denominator shrinks and the result grows rapidly. Small adjustments to either input therefore produce large valuation changes. This sensitivity is why sensitivity tables across both inputs are standard rather than optional with this method.
How does this method compare against an exit multiple approach?
This method derives terminal value from explicit long-run assumptions, which makes those assumptions visible and testable. The exit multiple approach derives it from observed market pricing, which embeds current conditions. Computing both and comparing them is common practice, and a large divergence indicates one set of assumptions is inconsistent with the other.
Related Reading
References
- SEC EDGAR: public company filings referenced when reviewing reported cash flow figures used as DCF forecast inputs.
- SEC: How to Read a 10-K: guidance on locating the cash flow statement figures analysts use to build forecast assumptions.
- CFA Institute Research and Policy Center: professional research on discounted cash flow and terminal value methodology.