Cross-Checking Exit Multiple Against Perpetuity Growth

There are two common ways to put a number on "everything after the explicit forecast ends" in a DCF. One is the Gordon growth perpetuity formula, built entirely from assumptions the analyst controls: a growth rate and a discount rate. The other is an exit multiple — take some future metric, usually EBITDA, and multiply it by a multiple observed in today's market for comparable companies, as if the business were sold at the end of the forecast period.

Both are trying to answer the same question, and they should land in the same neighborhood. When they don't, it's a signal that one of them is quietly assuming something the analyst never explicitly chose.

Running the crosscheck

Take the terminal EBITDA (or other metric) at the end of the explicit period, multiply it by a market-derived exit multiple to get the terminal value, then solve the Gordon growth formula backwards for the growth rate that would have produced that same terminal value:

$$g_{implied} = \frac{r \times TV - CF_n}{TV + CF_n}$$

In words: given the terminal value the exit multiple just produced, and the discount rate, back out what perpetual growth rate would justify that same number under Gordon growth. If that implied growth rate looks absurd — negative, or far above sustainable long-run growth — the exit multiple was a bad choice, or the market comparables it came from aren't as comparable as assumed.

Worked example

Year 5 EBITDA is forecast at $100 million. Comparable companies trade at 8x EBITDA, so the exit multiple approach gives a terminal value of $100m \times 8 = 800$ million. Year 5 free cash flow is $60 million, and the discount rate is 9%.

Solving for implied growth: $g = (0.09 \times 800 - 60) / (800 + 60) = (72 - 60)/860 = 12/860 \approx 1.4\%$. That's a modest, entirely plausible long-run growth rate — the 8x multiple passes the crosscheck.

Now suppose comparables actually trade at 12x instead: terminal value becomes $100m \times 12 = 1{,}200$ million. Implied growth: $g = (0.09 \times 1200 - 60)/(1200+60) = (108-60)/1260 = 48/1260 \approx 3.8\%$. Still plausible, though noticeably richer — worth asking whether those comparables are truly similar in growth and margin profile, or whether the multiple is importing an optimistic growth assumption that was never stated explicitly.

What this means in practice

Bankers often prefer the exit multiple method because it's grounded in an observable market number rather than a guessed growth rate — but "observable" doesn't mean "assumption-free." Running the implied growth crosscheck in both directions (and the reverse: what multiple does a chosen growth rate imply) is standard practice precisely because either method alone can hide an unreasonable number behind a familiar-looking format.