Fundamental growth rate formula

This is the wire that connects everything. It's the most important equation in fundamental analysis, and it's the test that catches the #1 amateur DCF sin.

How is the fundamental growth rate formula derived?

Start with the story. A company ends this year with NOPAT of ₹1,000 cr. It keeps back ₹400 cr, so its reinvestment rate RR is 40%. It deploys that into projects earning its return on invested capital, 15%. Next year those new projects add 400 × 15% = ₹60 cr of NOPAT. That's growth of 60 / 1,000 = 6%. Now look: 6% = 40% × 15% = RR × ROIC. Nothing else in the story produced growth. Only capital deployed at a return did.

Now the algebra. Let reinvestment_t = RR × NOPAT_t, and let new capital earn ROIC while returns on existing capital stay unchanged:

NOPAT_{t+1} = NOPAT_t + Reinvestment_t × ROIC = NOPAT_t × (1 + RR × ROIC)

⇒   g = RR × ROIC

g    = growth rate of NOPAT (operating income)
RR   = reinvestment rate = (capex − D&A + ΔWC) ÷ NOPAT
ROIC = return on invested capital = NOPAT ÷ invested capital  (marginal/incremental,
        strictly — the return on the NEW capital)

The equity version is the same logic one altitude down: g(EPS) = retention ratio × ROE, earnings kept back and deployed at the return on equity. You met b × ROE inside the Gordon model when you built the discounting machine. Now you know what it was.

What does the formula tell you about growth?

Three consequences follow at once, and each one is a valuation law:

1. Growth is bought, and the price is reinvestment. For a given ROIC, wanting more g means surrendering more of NOPAT to reinvestment: RR = g / ROIC. A company earning ROIC of 12% that wants to grow 9% must reinvest 75% of NOPAT. Only 25% is free cash flow. The same 9% growth at ROIC of 30% costs only 30% of NOPAT. So ROIC, question 2 of the five, is the quality variable. High-ROIC firms buy growth cheaply and pay out the rest. Low-ROIC firms consume themselves to grow. Later in the phase this gets pushed to its conclusion. At ROIC = WACC growth adds zero value, and below WACC growth destroys it.
2. Every growth forecast is secretly a ROIC claim. Type g into a revenue line and choose a reinvestment level, and you've asserted ROIC = g / RR whether you meant to or not. You can check that assertion against the company's history and its sector. The audit below does just that.
3. Efficiency growth is real but finite. Companies can grow briefly without reinvestment by filling idle capacity, squeezing working capital, or raising margins. Each of those lifts NOPAT off the existing capital base. Read in full, the formula is g = RR × ROIC_new + efficiency effects, and the second term has a ceiling. Utilization tops out at 100%, and margins hit sector gravity. Front-load efficiency gains in years 1 to 3 if the story earns them. But the growth that persists to your terminal year must be fully paid for by RR × ROIC. The terminal-value module enforces this at the terminal boundary, where it becomes non-negotiable.

How do you police a forecast with the formula?

Run the policing workflow on every forecast, yours or anyone's. It's the signature skill of the whole phase:

Step 1  From the model, read off:  g (NOPAT growth path),
        RR (reinvestment ÷ NOPAT), and the invested-capital line.
Step 2  Compute the implied ROIC two ways:
        · marginal: ΔNOPAT_t ÷ Reinvestment_{t−1}
        · book:     NOPAT_t ÷ IC_{t−1}   (the drift of this series over the forecast)
Step 3  Confront the implication with evidence:
        · vs the company's own achieved ROIC (5–10 yr, cyclically read)
        · vs the sector's ROIC distribution (Damodaran tables)
        · vs the moat verdict (Phase 4): sustained ROIC ≫ sector needs a named moat
Step 4  If implied ROIC is indefensible, the model is lying somewhere.
        Fix ONE lever: cut g, raise reinvestment, or (rarely, with evidence) defend
        the ROIC. Do not average your way out; pick the lever the story supports.

Worked example: a free-growth specialty-chemicals model

Here's the #1 amateur sin in action. An analyst models an Indian specialty-chemicals firm with NOPAT of ₹900 cr and a historical ROIC of 16%. They type in 15% growth for a decade while keeping capex ≈ D&A and WC flat. So reinvestment ≈ ₹150 cr/yr and RR ≈ 15%. The hidden claim is ROIC = g/RR = 15%/15% = 100%. The company supposedly mints ₹1 of new NOPAT for every ₹1 ever reinvested, six times its achieved 16%. Now the value effect. Proper reinvestment for 15% growth at 16% ROIC would be RR = 15/16 ≈ 94% of NOPAT, which leaves FCFF of ~₹56 cr instead of ~₹750 cr. The free-growth model overstates near-year free cash flow by roughly 13×.

This error, growth typed into the revenue line with no reinvestment attached, is the most common defect in student DCFs, promoter presentations, and a depressing share of sell-side models. The audit catches it in ninety seconds. It's also the deep reason the valuation sandbox has a consistency checker. The app will refuse the forecast. The market eventually does too.