Terminal value

You've met the growing perpetuity before. Here's the sixty-second rebuild, because every constraint that follows falls out of the derivation.

Say you own a claim paying CF₁ one year from now, growing at a constant rate g forever, discounted at rate r. Its value is the geometric series

PV = CF₁/(1+r) + CF₁(1+g)/(1+r)² + CF₁(1+g)²/(1+r)³ + …

Each term is the previous one multiplied by (1+g)/(1+r). Provided g < r, the series converges to:

PV = CF₁ / (r − g)          — the Gordon growth formula

Apply it at the end of your forecast horizon, year T, with FCFF as the cash flow and WACC as the rate:

TV_T = FCFF_T+1 / (WACC − g)         then discount: PV(TV) = TV_T / (1+WACC)^T

Three symbols, and each one comes with a rule. Watch the timing trap in the first. The numerator is the year T+1 cash flow, the first one the perpetuity actually pays, and year T's won't do. Grow it: FCFF_T+1 = FCFF_T-machinery grown one year. How you grow it is the subject of the reinvestment section below, and getting it wrong through the "free growth" shortcut is the most common DCF error in circulation.

How sensitive is terminal value to the growth rate?

Before the rules, get a feel for the formula's temper. At an 11% WACC, the terminal value equals FCFF_T+1 multiplied by:

The multiplier is 1/(WACC − g), and it's hyperbolic. Each half-point of g is worth more than the last. As g approaches WACC the value goes vertical, passes through infinity and, if g > WACC, comes out the other side as a negative number. Somewhere, a spreadsheet is reporting that number as a price target right now. So terminal g is the most abused input in finance, because it's the cheapest way to manufacture value. A junior analyst who needs 20% more value doesn't fabricate revenue. They nudge g from 4% to 5%, and nobody in the meeting blinks. Your defense is that the next two sections give g and its companions ceilings you can derive. Once those are in place, a nudge is a visible violation instead of a matter of taste.

Constraint 1: nothing outgrows the economy forever (deriving the g-cap)

Start with the intuition. The Gordon formula holds g constant forever. That means every term of an infinite series, far beyond year fifty. So ask what happens to a company that grows faster than its economy, forever. Take an economy growing at 8% nominal and a company growing at 12%. The company doubles relative to the economy every ~19 years. Run the tape. It passes 10% of GDP. Then it passes half. Then, by arithmetic it can't escape, it becomes the economy. After that it exceeds it, which is meaningless. Nothing rhetorical is going on here. Compounding does this on its own. So a perpetual growth rate above the economy's is a logical contradiction. People call it an aggressive assumption, and that's too kind. (Run it: over 200 years the relative size multiple is (1.12/1.08)^200 ≈ 1,440×. No world exists in which one firm is 1,440 times its starting share of everything.)

So: g ≤ long-run nominal growth of the economy the company earns in.

Why the risk-free rate is the practical cap. You need a number for "long-run nominal growth", and the best observable proxy is already in your WACC stack. It's the risk-free rate in your valuation's currency. The logic runs like this. A currency's long-run nominal risk-free rate ≈ expected long-run inflation + expected long-run real rate. Over long horizons the real rate and real growth converge toward each other, because capital earns roughly what the economy grows. When the two diverge for decades, one of them adjusts. That's the r vs g machinery you'll meet properly in Phase 7. The proxy is imperfect, but it has something no committee-chosen number has, and that's internal consistency. The same Rf is inside your WACC. Cap g at that Rf and WACC − g ≥ (WACC − Rf) = beta-weighted risk premium > 0, so your denominator can never go degenerate, in any currency, automatically. High-inflation currency? Then Rf is higher and the permitted g is higher, while the real assumptions don't change. The cap adjusts itself across currencies the way the Fisher relation says it must.

What terminal growth rate should you use?

The rule, and the numbers you'll use.

Terminal g ≤ risk-free rate used in your WACC stack (same currency, same number).
Most companies deserve less.

• US/USD models: Rf ≈ 4.2% (10-yr Treasury, as of mid-2026, check on FRED). Cap ≈ 4.2%. A typical mature company gets 2.5 to 3%, roughly inflation plus a sliver of real growth. A fading one gets less, possibly ≤ 0.
• India/INR models: use the cleaned INR Rf ≈ 4.5% from your WACC build (6.5% G-sec − 2.0% default spread, as of mid-2026, check both on RBI/CCIL and Damodaran's ctryprem page), so the cap ≈ 4.5%. Nicely, 4.5% ≈ RBI's 4% inflation target plus ~0.5% real. That's a sensible nominal growth rate for the mature India of the 2050s, and the mature state is what the terminal value describes. Some practitioners build the WACC on the raw 6.5% G-sec instead. If you do, your cap is 6.5%. The rule is about consistency with your own stack, and there's no magic number. What you may never do is take one number from each stack. Put a cleaned 4.5% risk-free rate inside the WACC and a 6.5% cap on g, and you've handed growth the sovereign default spread the discount rate was just cleaned of. On the cement build, that one inconsistency lifts the terminal value 8.0% and the enterprise value 5.1%. Whichever stack you pick, take both numbers from it. Wherever else you meet a terminal cap, it means this rule and this stack.

Three refinements experts carry:

1. The terminal state is decades away, so assume the mature economy. India grows ~10 to 11% nominal today. Your terminal year is 2036 or later, and it describes a company in a much richer, slower India. So today's growth belongs in the explicit period, and if the runway is long, extend the horizon. The terminal g describes maturity.
2. g can be below inflation, zero, or negative. A perpetuity doesn't promise growth. Tobacco volumes are the classic case. Landline telephony and print media are in the same position. For businesses like these, the right input is sometimes negative real terminal growth. It can even be negative in nominal terms, and the formula handles that fine: WACC − (−2%) just widens the denominator.
3. Match g to the currency of the model, whatever flag flies over headquarters. A US-listed company valued in INR terms takes the cap of the model currency, and the same goes the other way round. It's the same Fisher logic as station 1 of your WACC build.

Constraint 2: growth is never free (terminal reinvestment)

Here's the error that inflates more DCFs than any other. An analyst finishes year 10 with FCFF = ₹14,284 cr and computes TV = 14,284 × 1.045 / (0.11 − 0.045). Five seconds, done. It's also wrong, in the flattering direction, by a margin we'll put at roughly half the terminal value.

So what's wrong with it? Growing at 4.5% forever needs investment forever: new capacity, working capital, stores, servers. FCFF is what's left after that reinvestment. Grow the post-reinvestment cash flow at g while assuming reinvestment stays frozen, or worse, that year 10's reinvestment level was temporary, and you've conjured growth that consumes no capital. That's free growth. You already have the identity that forbids it:

g = reinvestment rate × ROIC        ⇒        reinvestment rate (RR) = g / ROIC

In steady state, a company that grows NOPAT at g while earning ROIC_terminal on new capital has to plow back g / ROIC_terminal of NOPAT every year, forever. So you build the terminal cash flow from NOPAT instead of growing it from FCFF:

FCFF_T+1 = NOPAT_T+1 × (1 − g / ROIC_terminal)
TV_T     = NOPAT_T+1 × (1 − g / ROIC_terminal) / (WACC − g)

This is the only legitimate Gordon numerator. Look at what it does. Growth now has a price, and the quality of the business sets that price. A company that earns ROIC_terminal = 20% buys 4.5% growth for 22.5% of NOPAT. A company earning 9% must pay 50% of NOPAT for the same growth. Quality, in other words, is the capital efficiency of growth. That one fraction holds the whole ROIC-versus-WACC way of seeing a business.

Worked example: what reinvestment does to terminal value

Worked contrast, using the UltraTech-style cement build. Year-10 NOPAT ₹20,035 cr, so NOPAT₁₁ = 20,035 × 1.045 = ₹20,937 cr. WACC 11%, g 4.5%.

Ignoring terminal reinvestment overstates this terminal value by 60% against the defensible 12%-ROIC line. And by construction the error is always an overstatement. No wonder it survives so comfortably in bullish research.

Now look again at the first row, because there's a punchline hiding in it. Set ROIC_T equal to WACC and simplify:

TV = NOPAT_T+1 × (1 − g/WACC) / (WACC − g)
   = NOPAT_T+1 × ((WACC − g)/WACC) / (WACC − g)
   = NOPAT_T+1 / WACC          — g has vanished.

When ROIC = WACC, growth is worthless. Grow at 0%, 3% or 4.5% and the value is identical. Check it in the table: 1,90,336 = 20,937/0.11 exactly. Every rupee of value that new growth creates is paid for, in full, by the capital that buys it. You're looking at McKinsey's key-value-driver formula, Value = NOPAT_T+1 × (1 − g/ROIC) / (WACC − g), read at its fixed point, and it holds the deepest sentence in corporate finance. Growth creates value only at positive spreads. At ROIC = WACC growth is cosmetic, and at ROIC < WACC growth actively destroys value, pushing the formula below the no-growth perpetuity. The next section shows that with numbers. Value creation gets a full treatment of its own in Value drivers and capital allocation. Here it does a narrower job, as the rule for the terminal value.

Constraint 3: competitive advantage decays (where ROIC_terminal comes from)

The table above shows TV swinging ₹60,000 cr on the choice of ROIC_terminal. So what number is defensible?

Start from an empirical fact you'll prove to yourself in Phase 4: excess returns mean-revert. High-ROIC companies attract capital, competitors, imitators, regulators and unionizing suppliers. A 40% ROIC is a standing invitation for the rest of capitalism to come and take it. Mauboussin's persistence studies, and McKinsey's decay curves, show cohorts of high-ROIC firms drifting toward the middle over 10 to 15 years. On average they don't get all the way to zero spread, because moats are real. But they drift toward it, relentlessly. The terminal value describes your company in a steady state decades from now, after this decay has run its course.

The default and the exceptions:

Default:            ROIC_terminal = WACC           (competition wins; growth becomes cosmetic)
Defensible premium: ROIC_terminal = WACC + 1–4 pts (a NAMED, Phase-4-graded moat: brand pricing
                                                    power, network effects, regulated position,
                                                    switching costs with proof in ROIC persistence)
Never:              ROIC_terminal = today's 35–50% (assumes the moat outlives every empire
                                                    in recorded history)

Rules of engagement:

1. Name the premium. A feeling won't do. "It's a great company" buys nothing. "Nestlé-grade brands have held gross margins for 60 years across geographies; I grant ROIC_T = WACC + a wide premium" is an argument. You'll be able to grade it after Phase 4, and the mastery check will ask you to make one like it.
2. Let the spread fade, which doesn't necessarily mean fading the ROIC's level. In practice you build in decay by choosing ROIC_T well below the current ROIC and letting the explicit period glide toward it, the same fade you used in your forecasts. A company at 45% today might get ROIC_T = 20%. That's still a fat spread, reflecting a real moat, but it's half-decayed.
3. Mind the accounting mirage. Capital-light compounders (IT services, FMCG, software) show measured ROICs of 40 to 90%. Part of the reason is that their real assets were expensed instead of capitalized: the brands, the code, the trained people. Their incremental economics are superb, but they aren't infinite. Sales-to-capital keeps the reinvestment realistic even when the ROIC ratio looks silly.
4. Symmetry. Sub-WACC businesses in the terminal year, such as airlines or commodity cyclicals mid-cycle, do one of three things. They restructure toward WACC, they shrink (negative g with capital release), or they exit. Modeling ROIC_T < WACC with positive growth forever asserts that management will destroy value at a constant rate for eternity. That's occasionally true, but say it out loud before you type it. (Try ROIC_T = 8% in the reinvestment table above: RR = 56.3%, TV = ₹1,40,922 cr. That's below the zero-growth ₹1,90,336 cr, as the key-value-driver formula demands.)

How do you check the terminal year is a steady state?

The steady-state audit. "Terminal year" means the company has arrived. So before you capitalize year T, audit it against this list, which the mastery check also tests:

• Growth at or below the cap, and equal to the g in your TV formula, so year T's growth runs straight into the perpetuity's without a jump.
• Reinvestment = g/ROIC_T of NOPAT. Mechanically, that means capex modestly above D&A, because a steady-state firm growing at g replaces its assets and adds a g-sized increment. It also means working capital scaling with revenue. A terminal year with capex < D&A forever is a liquidation wearing a growth rate.
• Margins flat. The expansion story is finished, and if it isn't, your horizon is too short.
• Tax at the marginal statutory rate, the rule from your WACC build. Holidays and loss carryforwards belong to the explicit period.
• ROIC on incremental capital = ROIC_T by construction. Check that the level is one you can defend.