The Gordon Growth Terminal Value

A DCF forecasts a handful of years in detail, then has to answer an uncomfortable question: what is every cash flow after that, stretching to infinity, worth today? Forecasting year by year forever is impossible, but the value of those distant years is often more than half the entire valuation — so it can't just be ignored. The Gordon growth model collapses that infinite, unknowable stream into one closed-form number, using a single assumption: cash flow grows at a constant rate, forever, after the explicit forecast ends.

The formula

$$TV_n = \frac{CF_{n+1}}{r - g} = \frac{CF_n \times (1+g)}{r-g}$$

In words: take the cash flow expected in the first year after the explicit forecast ends, and divide it by the discount rate minus the perpetual growth rate. That single number represents the present value, as of the end of the forecast period, of every cash flow from then to forever — it still needs to be discounted back to today from year $n$, not treated as already being in today's dollars.

Why the growth rate must be small and sane

The formula only produces a sensible, finite, positive answer when the discount rate $r$ is larger than the growth rate $g$. Beyond that mechanical requirement, $g$ represents a growth rate a company can sustain forever, which rules out anything resembling recent high growth — no real company can outgrow the overall economy indefinitely without eventually becoming larger than the economy itself. In practice $g$ is usually capped near a long-run GDP or inflation growth rate, often 2-4%.

Worked example

The explicit forecast's final year (year 5) produces a free cash flow of $50 million. The analyst assumes 3% perpetual growth thereafter, and the discount rate is 9%.

Next year's cash flow: $CF_6 = 50m \times 1.03 = 51.5$ million. Terminal value at year 5: $TV_5 = 51.5 / (0.09 - 0.03) = 51.5 / 0.06 \approx 858.3$ million. That figure is still five years in the future, so it must be discounted back to today at 9% over 5 years: $858.3 / 1.09^5 \approx 858.3 / 1.539 \approx 557.7$ million — the present value the terminal value actually contributes to today's valuation.

Now compare: if the growth assumption were bumped from 3% to 5%, terminal value at year 5 becomes $50m \times 1.05 / (0.09-0.05) = 52.5/0.04 = 1{,}312.5$ million — a 53% jump in terminal value from a growth assumption that still looks modest on paper.

What this means in practice

Because terminal value routinely makes up 60-80% of a DCF's total value, the $g$ assumption deserves more scrutiny than almost any other input in the model, even though it's often the one filled in last and fastest.