Normalising the Terminal Year in a DCF: Why Capex Must Converge to Depreciation, and Why the Reinvestment Rate — g ÷ ROIC — Is What Actually Pins the Perpetuity

The Terminal Year Is Not the Last Forecast Year Times One Plus g

The terminal value carries most of a DCF — commonly 60-80% of the enterprise value in a five-year model — so the single cash flow it is built on deserves more scrutiny than any explicit forecast year. That cash flow is the normalised terminal free cash flow: what the business generates once it has stopped scaling and settled into a steady state it can hold forever. It is emphatically not the last modelled year grown by one growth increment.

The distinction matters because the explicit forecast is usually a period of change — margins expanding, capex elevated to fund a build-out, working capital swinging with the top line. Freezing that final, still-transitioning year and compounding it into perpetuity bakes a temporary state into an eternal one. The perpetuity assumes constancy; the terminal-year inputs have to be set to something actually constant before the Gordon growth or exit-multiple formula is applied.

The g = 0 Sanity Check: Capex Must Equal Depreciation

Start with the cleanest case: a company that has stopped growing, g = 0. In that world the asset base is constant, so the cash spent replacing worn-out assets — capex — must exactly match the accounting charge for that wear, depreciation. Spend less than depreciation every year forever and the fixed-asset base erodes to zero; spend more and the assets are growing, which contradicts zero growth. Net capex is therefore zero, the change in working capital is zero, and terminal free cash flow equals NOPAT — EBIT after tax, and nothing subtracted.

This is the sanity check every terminal year should pass through first. If a model’s terminal year shows capex running well below depreciation while assuming perpetual growth, it is generating cash by quietly liquidating the company — a cash flow no buyer would pay for. The “capex should roughly equal depreciation in the terminal year” rule interviewers repeat is exactly this g = 0 identity, and it is a floor, not the full answer.

With Growth, Capex Must Exceed Depreciation — and the Reinvestment Rate Is g ÷ ROIC

The heuristic breaks the moment terminal growth is positive. A company growing NOPAT at 2.5% forever cannot do so on replacement capex alone — it has to add capacity, which means gross capex above depreciation, plus a permanent trickle of working-capital investment. Setting capex = depreciation with g > 0 understates reinvestment and overstates free cash flow. The question is how much reinvestment growth requires, and there is an exact answer.

Growth is bought with reinvested capital, and the price is the return that capital earns. The identity is reinvestment rate = g ÷ ROIC, where ROIC is the return on the incremental invested capital. Terminal free cash flow is then NOPAT × (1 − g/ROIC). A firm growing at 2.5% that earns a 12.5% return on new capital must plough back 2.5% ÷ 12.5% = 20% of NOPAT to fund that growth, and only the remaining 80% is free.

Same NOPAT, same growth, same discount rate — and a 28% gap in the terminal value, driven entirely by whether the model made growth pay for its own reinvestment. The naive column is not conservative or aggressive by accident; it is wrong, because it books 2.5% perpetual growth while spending nothing to produce it.

The Silent Error: Growing a Cash Flow That Has Not Reinvested

The reason this mistake survives review is that both numbers look reasonable in isolation. £76.9M is a perfectly plausible free cash flow, and 2.5% is a defensible growth rate — the error is in their combination, not either input. A reviewer scanning the terminal year sees a sensible cash figure and a sensible growth figure and moves on, never asking the one question that exposes it: what reinvestment rate does this cash flow imply?

Back out the implied reinvestment and the naive column confesses. Growing NOPAT at 2.5% while distributing 100% of it means reinvestment is zero, which means the implied ROIC is infinite — the company grows forever on no new capital. That is not a bullish assumption; it is an impossible one. Forcing the reinvestment rate to be explicit, via g ÷ ROIC, is what turns an invisible error into a line a reviewer can challenge.

If ROIC Equals WACC, Growth Is Worthless — and the Terminal Value Collapses to NOPAT ÷ WACC

The reinvestment form exposes a second truth the naive form buries: terminal growth only creates value when the company earns more on new capital than that capital costs. Substitute ROIC = WACC into the terminal value and the algebra is unambiguous — NOPAT × (1 − g/WACC) ÷ (WACC − g) simplifies to NOPAT ÷ WACC, independent of g. Growth at the cost of capital adds nothing.

This is the strongest sensitivity check available on a terminal value. Nudging g from 2% to 3% in a naive model always lifts the valuation, which tempts analysts to treat g as a dial for the answer they want. In a properly reinvested model, raising g raises reinvestment in lockstep, and the net effect on value depends solely on the ROIC-versus-WACC spread. A high terminal g is only worth having if the company is a genuine value creator — and the model should say so, not launder growth into value for free.

Working Capital Does Not Stop Investing in Perpetuity Either

Fixed capital is the visible half of terminal reinvestment; working capital is the half that gets dropped. A business growing revenue at g needs its net working capital to grow at g too — more receivables, more inventory — and that incremental investment is a real cash outflow every year forever. The g ÷ ROIC reinvestment rate already captures this if ROIC is defined on total invested capital, but analysts who build the terminal year bottom-up from capex and depreciation routinely forget the working-capital line and overstate cash by the amount of it.

The discipline is to reconcile the two approaches. Build terminal FCF as NOPAT − net capex − increase in NWC, then check that the implied reinvestment rate matches g ÷ ROIC. If the bottom-up cash flow implies a 5% reinvestment rate while the growth-and-return assumptions demand 20%, the terminal year is internally inconsistent — and the inconsistency is almost always a forgotten investment line inflating the cash flow.

The Verdict: Normalise the Numerator Before Arguing About the Denominator

The terminal value is where a DCF is won or lost, and the fight is on the wrong side of the fraction. Analysts pour hours into the discount rate and the growth rate — the denominator of the perpetuity — while the cash flow in the numerator is set by reflex to last-year-times-one-plus-g. That reflex assumes perpetual growth at zero reinvestment cost, the single most value-inflating assumption a model can make, and it is invisible precisely because the resulting cash figure looks ordinary.

The fix costs one line. Pin the terminal cash flow to NOPAT × (1 − g/ROIC), sanity-check it against the g = 0 case where capex equals depreciation and FCF equals NOPAT, and confirm the working-capital investment is still there. Do that and the terminal value stops being a number the model backs into and starts being one it can defend — which is the difference between a DCF that describes a business and one that flatters it.

How It Is Tested in Interviews

The question is usually phrased as a trap: “In the terminal year, what should capex be?” The weak answer is “equal to depreciation” and stops there. The strong answer names the condition — capex equals depreciation only when terminal growth is zero, and with positive growth capex must exceed depreciation to fund it. Then it produces the number: reinvestment rate = g ÷ ROIC, so terminal FCF = NOPAT × (1 − g/ROIC). If pushed on why it matters, close with the ROIC = WACC point — growth only creates value above the cost of capital, and a model that grows an unreinvested cash flow assumes value from growth that is not there.

Take Your Preparation Further

For the two ways to compute the terminal value once the cash flow is normalised, see DCF Terminal Value: Gordon Growth vs Exit Multiple. For the cash-flow definition the terminal year is built from, see Unlevered Free Cash Flow and From EBITDA to Free Cash Flow. For the discount rate on the other side of the fraction, see The WACC Calculation, and for how the whole thing is assembled under interview pressure, Walk Me Through a DCF.

Download the free Valuation Methods Cheat Sheet, and build the mechanics yourself with the DCF Model Template, which sets the terminal year off a reinvestment rate rather than a flat cash flow.

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