DCF Valuation Example: The Perpetuity (Gordon Growth) Method
The fastest DCF an analyst runs isn't a ten-tab spreadsheet — it's a single line on a napkin: value = FCF / (r − g). Master this gut-check and you can sanity-check any valuation in seconds.
Why this matters
Why interviewers probe the perpetuity
A full discounted cash flow model projects free cash flow year by year, discounts each flow to today, and then bolts on a terminal value to capture everything beyond the explicit forecast. That terminal value is almost always the Gordon growth perpetuity — so if you understand the one-line version, you understand the engine that drives most of a DCF's output.
The Gordon growth model values a stream of cash flows that grows forever at a constant rate. Take next year's free cash flow, divide by the discount rate minus the growth rate, and you have a present value. Interviewers love it precisely because it is compact: there is nowhere to hide. If you fumble whether growth belongs in the numerator or denominator, or why the value explodes as growth approaches the discount rate, it shows immediately.
This guide walks one clean example end to end, shows how sensitive the answer is to your assumptions, and then hands you a graded drill so the arithmetic becomes automatic.
Worked example
One perpetuity, start to finish
The inputs
- Next-year free cash flow (FCF)$120M
- Discount rate (WACC), r10%
- Perpetual growth rate, g2%
Step 1 — Find the value
Plug straight into the Gordon growth formula. The spread r − g is the only thing in the denominator:
Value = 120 / (0.10 − 0.02)
Value = 120 / 0.08 = $1,500M
Step 2 — Read the implied FCF multiple
Because value equals FCF divided by the spread, the multiple you are paying on next-year free cash flow is just the reciprocal of that spread:
Implied multiple = 1 / 0.08 = 12.5x
A 12.5x forward-FCF multiple is a sanity anchor. If comparable companies trade at 9x and your perpetuity spits out 20x, your r or g is doing something you can't defend.
Step 3 — Stress the discount rate
Now nudge WACC up by a single percentage point, from 10% to 11%, and hold growth fixed. The spread widens from 8% to 9%:
New value = 120 / 0.09 ≈ $1,333M
One point of WACC just erased roughly $167M — about 11% of the company's value — without touching a single cash-flow assumption. That is the whole lesson in one number.
The intuition
Why small changes swing value so hard
The culprit is the shape of 1 / (r − g). When the denominator is small, dividing by it magnifies everything — and it gets more violent as r − g shrinks toward zero. At a spread of 8% you pay 12.5x. Tighten the spread to 6% and you pay 16.7x; widen it to 10% and you pay only 10x. The relationship is not linear, it is a hyperbola, so the same one-point move matters far more when r and g are already close together.
This is also why terminal growth assumptions get scrutinized so hard. Analysts cap perpetual growth near long-run GDP (2–3%) not out of habit but because pushing g up half a point when r is only a few points higher can inflate value dramatically. The math rewards optimism far more than it should, which is exactly why a disciplined analyst keeps g conservative.
In a full multi-stage DCF, this leverage lives inside the terminal value. You discount five to ten years of explicit free cash flows, then apply this same perpetuity to the final forecast year to capture the rest — and discount that lump sum back to today. Because terminal value routinely accounts for 60–80% of total enterprise value, the r − g spread you pick for the perpetuity quietly controls most of your answer. Nail the gut-check and the big model stops surprising you.
Watch out
Common mistakes
Letting g creep up to (or past) r
If perpetual growth equals the discount rate, the denominator is zero and value is infinite; if g exceeds r, value goes negative and meaningless. A perpetuity growing faster than its discount rate forever is economically impossible — no company outgrows the whole economy indefinitely. Keep g below r, and realistically at or under long-run GDP growth.
Mixing levered and unlevered cash flow
Unlevered free cash flow (to the whole firm) is discounted at WACC to get enterprise value. Levered free cash flow (to equity) is discounted at the cost of equity to get equity value. Pairing unlevered FCF with the cost of equity — or the reverse — is one of the fastest ways to blow an interview. Pick a lane and keep the numerator and discount rate consistent.
Letting terminal value dominate unchecked
It is normal for terminal value to be the majority of enterprise value, but if it's 90%+ of the total your explicit forecast is doing almost no work. Always back into the implied exit multiple your perpetuity produces and compare it to trading comps. If the implied multiple is absurd, revisit r and g rather than trusting the output.
Using the wrong year's FCF
The Gordon growth formula uses next year's cash flow in the numerator — the first flow of the perpetuity, not the current year. Plugging in the trailing figure understates value by one period of growth. Confirm you are one step ahead.
FAQ
Frequently asked questions
What is the Gordon growth (perpetuity) DCF formula?
Value = FCF / (r − g), where FCF is next year's free cash flow, r is the discount rate (WACC), and g is the perpetual growth rate. It values a cash flow stream that grows forever at a constant rate. With FCF of $120M, r of 10%, and g of 2%, value = 120 / (0.10 − 0.02) = $1,500M.
Why does a DCF value change so much when I tweak WACC or growth?
Because value scales with 1 / (r − g), a small denominator. When r − g is 8%, the implied multiple is 12.5x. Raise r by one point so the spread becomes 9% and the multiple drops to 11.1x — an ~11% fall in value from a one-point change. The closer g gets to r, the more violent the swing.
What is the implied FCF multiple in a perpetuity DCF?
It is simply 1 / (r − g). With r = 10% and g = 2%, the implied multiple is 1 / 0.08 = 12.5x next-year FCF. This is a fast sanity check: if the perpetuity multiple looks unreasonable versus trading comps, your r or g assumptions are probably off.
How does the perpetuity gut-check relate to a full multi-stage DCF?
In a full DCF you project explicit free cash flows for 5–10 years, then capture everything after with a terminal value. The most common terminal value method is exactly this Gordon growth perpetuity applied to the final-year FCF, then discounted back. Terminal value often drives 60–80% of total enterprise value, so the same r − g leverage dominates the whole model.
What are the most common DCF mistakes interviewers look for?
Setting perpetual growth g at or above the discount rate r (which breaks the formula), mixing levered and unlevered free cash flow with the wrong discount rate, assuming a terminal growth rate above long-run GDP, and letting terminal value silently dominate enterprise value without sanity-checking the implied exit multiple.
Now make the math automatic
Reading a worked example is one thing — doing it under a timer is another. Run the graded DCF gut-check drill with fresh numbers every attempt, or build the full model with live data.