06.1 · What value is¶

Why this matters: every technique in this module — DCF, multiples, reverse DCF, residual income — is a way of computing one quantity: the present value of the cash a business will hand its owners. If you understand that quantity and what drives it, the techniques are bookkeeping. If you don't, the techniques become rituals that produce whatever number you wanted. This lesson is the short, rigorous foundation: value = cash, discounted; and the three things that move it are growth, return on capital and risk.

Learning objectives — after this lesson you can:

Define intrinsic value and distinguish it from price, book value and relative value.
Derive the value-driver formula \(V = \frac{\text{NOPAT}_1(1 − g/\text{ROIC})}{\text{WACC} − g}\) from a growing perpetuity, and use it to show that growth creates value only when ROIC > WACC.
Explain why a great company can be a bad investment and a mediocre company a good one.
Separate price, value and expectations, and state what an investor actually bets on.
Compute the steady-state value of Kaveri Pumps from the formula and reconcile it with the full DCF.

Prerequisites: 01.5 Time value of money, 04.3 Returns on capital · Time: ~75 min

1. Three kinds of "value"¶

Term	Definition	What it is good for	What it is not
Intrinsic value	The present value of all future cash flows the asset will deliver to its owner, discounted at a rate reflecting their risk	The anchor; the number you compare price with	Observable. It is an estimate with a distribution, not a point
Relative value	What similar assets are priced at (multiples)	A cross-check; a way to see what the market pays for comparable growth/returns	A substitute for intrinsic value — if the peers are mispriced, so is the comparison
Book value	Accounting equity: assets − liabilities at (mostly) historical cost	A floor for asset-heavy businesses and lenders; the base for ROE	A measure of what the business is worth — brands, people and franchises are not on it
Price	What the last buyer paid	The thing you compare value with	Value. Price is set by the marginal trade; value by the cash flows

John Burr Williams (1938) wrote the definition that still stands: the value of any asset is the present value of its future cash flows. For a bond the cash flows are contractual; for a share they are the dividends and buybacks the company will pay over its life (equivalently, the free cash flows it generates, since those must eventually be paid out or reinvested to produce later payouts).

\[V_0 = \sum_{t=1}^{\infty} \frac{CF_t}{(1+r)^t}\]

Everything else in valuation is about estimating \(CF_t\) and \(r\), and about the shortcuts (multiples, perpetuities) that make the infinite sum tractable.

2. The value-driver formula¶

Start with the growing perpetuity from 01.5: a cash flow of \(CF_1\) next year, growing at \(g\) forever, discounted at \(r\), is worth

\[V_0 = \frac{CF_1}{r − g} \qquad (g < r)\]

For a business, the cash flow to all capital providers is free cash flow to the firm: operating profit after tax (NOPAT) minus the reinvestment needed to grow. From the reinvestment identity in 04.3, to grow NOPAT at rate \(g\) with a return on new capital of ROIC you must reinvest a fraction \(g/\text{ROIC}\) of NOPAT:

\[\text{FCFF}_1 = \text{NOPAT}_1 − \text{Reinvestment}_1 = \text{NOPAT}_1\left(1 − \frac{g}{\text{ROIC}}\right)\]

Substitute into the perpetuity, with \(r = \text{WACC}\):

\[\boxed{V_0 = \frac{\text{NOPAT}_1 \left(1 − \dfrac{g}{\text{ROIC}}\right)}{\text{WACC} − g}}\]

This is the value-driver formula (McKinsey's name; the "key value driver" formula). Three inputs — growth, return on invested capital, cost of capital — and one line of algebra. It is the most important equation in the course, because it makes precise a claim most investors only hold as intuition.

2.1 Growth only creates value when ROIC > WACC¶

Divide both sides by NOPAT to get the value multiple \(V/\text{NOPAT}\), and tabulate it for a WACC of 12%:

ROIC \ g	0%	3%	6%	9%
8% (< WACC)	8.3x	6.9x	4.2x	−4.2x (nonsense: growth needs more reinvestment than NOPAT)
12% (= WACC)	8.3x	8.3x	8.3x	8.3x
16%	8.3x	9.0x	10.4x	14.6x
24%	8.3x	9.7x	12.5x	20.8x
40%	8.3x	10.3x	14.2x	25.8x

w = 0.12
for roic in (0.08, 0.12, 0.16, 0.24, 0.40):
    print(roic, [round((1 - g / roic) / (w - g), 1) for g in (0.0, 0.03, 0.06, 0.09)])

Read the middle row first. When ROIC equals WACC, the value multiple is 1/WACC = 8.3x regardless of growth. Growing at 9% is worth exactly the same as not growing at all, because every rupee reinvested to produce the growth earns just its cost — the new capital is worth what it cost, no more. Now read down the columns: at ROIC above WACC, faster growth raises the multiple, steeply; at ROIC below WACC, faster growth lowers it. A company earning 8% on capital that grows at 6% is worth half as much as the same company standing still.

This is why 04.3 insisted on incremental ROIC, why 05.3 called the moat the largest input to the terminal value, and why "growth stock" and "value stock" is a false dichotomy: growth is an input to value, with a sign that depends on ROIC.

2.2 Kaveri in steady state¶

Kaveri's FY26 NOPAT is ₹100.3 Cr. Suppose the company were already in its terminal state — growing 5.5% a year for ever with a 12.19% WACC (the reference valuation's inputs) — and ask what value different terminal ROICs imply:

nopat = 100.3; w = 0.1219; g = 0.055
for ronic in (0.12, 0.15, 0.18, 0.25):
    v = nopat * (1 + g) * (1 - g / ronic) / (w - g)
    print(ronic, round(v), round((v - 140.5 - 18.2) / 6.07))
# 0.12 → EV ≈ 857, ≈ ₹115/share
# 0.15 → EV ≈ 1,001, ≈ ₹139/share
# 0.18 → EV ≈ 1,098, ≈ ₹155/share
# 0.25 → EV ≈ 1,234, ≈ ₹177/share

Two lessons. First, the assumed return on new capital moves the value by 50% across a plausible range — that is the moat judgement, in rupees. Second, all of these are far below the ₹320 base case and the ₹390 price, which tells you that most of Kaveri's value in the full DCF comes from the explicit forecast years of 10–14% growth at rising margins, not from the steady state. 06.3 builds that forecast; 06.6 asks whether the price already assumes it.

3. Price, value and expectations¶

Ben Graham's formulation: price is what you pay, value is what you get. The modern refinement (Rappaport and Mauboussin, Expectations Investing) adds a third object: the expectations embedded in the price. A stock price is a forecast — it is the value that results from some set of assumptions about growth, ROIC and risk. You do not need to know intrinsic value with precision; you need to know whether the market's implied assumptions are too high or too low.

Object	How you get it	What you do with it
Price	Observe	—
Your estimate of value	Forecast cash flows; discount	Compare with price; size the gap against your uncertainty
Market's implied expectations	Solve the DCF backwards for the growth/margin that justifies the price	Ask: is that forecast plausible? Where specifically do I disagree?

Trader's lens

This is exactly the implied-vs-realised structure of options. Nobody prices an option by forecasting the payoff; they back out the implied vol and ask whether realised vol will be higher or lower. A share price backs out implied growth (and implied ROIC persistence). Your edge is a view on realised growth vs implied — and, as with vol, the view is only worth expressing when the gap is large relative to your estimation error. Reverse DCF (06.6) is the implied-vol calculator for equities.

4. Why a great company can be a bad investment¶

Take a business with ROIC of 40% and growth of 9% — the top-right cell, 25.8x NOPAT. If the market prices it at 50x NOPAT, the buyer is paying for a return-and-growth combination that the formula cannot produce at a 12% WACC: they need ROIC to stay at 40% and growth to exceed 9% for decades, or the cost of capital to be much lower. If instead growth fades to 6% (still excellent), the multiple should be 14.2x — the investor loses 70% of their money while the company keeps compounding beautifully. Cisco in 2000 (case G3) and Asian Paints at 80x in 2021 (case I2) are this cell.

The mirror image: a business with 14% ROIC and 4% growth is worth ~8.9x NOPAT; priced at 6x because it is boring and out of favour, it offers a 50%+ return to fair value without any heroics. Coal India at single-digit P/Es in 2020–22 had this profile. "Quality" is not a valuation; it is an input.

5. What is not in the formula — and where it hides¶

Risk appears only through WACC. In practice you handle it three ways: in the discount rate (systematic risk), in the cash-flow scenarios (business-specific risk; 06.4), and in the margin of safety you demand between value and price (06.8). Never in all three at once for the same risk.
Time to fade: the formula assumes ROIC and g are constant for ever. Real companies fade toward WACC; the DCF's explicit period plus a terminal assumption is how you model the path.
Non-operating assets and claims: cash, investments, debt, leases, minorities, options — the bridge from enterprise value to equity value per share (06.3).
Inflation: g and WACC must be in the same terms (both nominal ₹ or both real). Indian valuations are almost always nominal ₹ with a 5–6% terminal g reflecting ~4% inflation plus modest real growth.

6. Worked example — two companies, one formula¶

Sahyadri Bearings (fictional): NOPAT next year ₹120 Cr, ROIC on new capital 20%, sustainable growth 6%. Tapti Textiles (fictional): NOPAT next year ₹120 Cr, ROIC 9%, growth 6%. Both have WACC 12%, net debt ₹200 Cr, 10 Cr shares.

def value(nopat1, roic, g, wacc=0.12, net_debt=200, shares=10):
    ev = nopat1 * (1 - g / roic) / (wacc - g)
    return round(ev), round((ev - net_debt) / shares)
print(value(120, 0.20, 0.06))   # EV 1,400 → ₹120/share
print(value(120, 0.09, 0.06))   # EV 667  → ₹47/share
print(value(120, 0.09, 0.00))   # EV 1,000 → ₹80/share  (Tapti is worth MORE if it stops growing)

Same profit, same growth, same risk; Sahyadri is worth 2.5x Tapti per share — and Tapti's shareholders would be ₹33/share better off if management stopped expanding. That last line is the practical content of the formula: for a sub-WACC business, the best capital allocation is to return cash, and a "growth strategy" is value destruction with a press release (05.5).

Common mistakes

Using the formula with g ≥ WACC (infinite value) or g > ROIC (negative reinvestment) — both are input errors.
Applying a high multiple to "quality" without checking that the ROIC–growth combination justifies it.
Treating book value as a floor for a business that burns cash — book value can go to zero.
Forgetting that NOPAT in the numerator is next year's, and that reinvestment is already netted out (do not subtract capex again).
Mixing real growth with a nominal discount rate.

Key terms¶

Term	Meaning
Intrinsic value	Present value of all future cash flows to the owner, at a risk-appropriate discount rate
Relative value	Value inferred from the prices of comparable assets (multiples)
Growing perpetuity	\(CF_1/(r − g)\): the value of a cash flow growing at g for ever
Free cash flow to the firm (FCFF)	NOPAT + D&A − capex − ΔNWC: cash available to all capital providers
Reinvestment rate	Share of NOPAT reinvested = g / ROIC in steady state
Value-driver formula	\(V = \text{NOPAT}_1(1 − g/\text{ROIC})/(\text{WACC} − g)\)
Value multiple	\(V/\text{NOPAT}\); equals \(1/\text{WACC}\) when ROIC = WACC
RONIC	Return on new invested capital, the ROIC that matters for growth's value
Expectations (implied)	The growth/return assumptions that make a DCF equal the market price
Fade	The decline of ROIC toward WACC over time as competition acts
Margin of safety	The gap between estimated value and price demanded to absorb estimation error

Check your understanding¶

A company has ROIC = WACC = 11%. Management announces a plan to double growth from 4% to 8% by reinvesting more. What happens to value?

Answer

Nothing. With ROIC = WACC the value multiple is 1/WACC = 9.1x NOPAT whatever the growth rate; the extra reinvestment earns exactly its cost. Shareholders should be indifferent — and suspicious of the effort, since executing growth carries risk for no reward.

Using the value-driver formula, what value multiple does a company with ROIC 30%, g 7%, WACC 12% deserve? What if the market prices it at 35x NOPAT — what is it assuming?

Answer

(1 − 0.07/0.30)/(0.12 − 0.07) = 0.767/0.05 = 15.3x. A 35x price implies (holding ROIC at 30%) g ≈ 10.1% for ever, or (holding g at 7%) a WACC of ~9.2%, or some combination — each of which is far outside anything the formula finds plausible as a perpetuity.

Recompute Kaveri's steady-state value per share with RONIC 18% but g of 4% instead of 5.5%.

Answer

EV = 100.3 × 1.04 × (1 − 0.04/0.18)/(0.1219 − 0.04) = 104.3 × 0.778/0.0819 = ₹991 Cr; equity = 991 − 158.7 = 832; per share ≈ ₹137 — lower than at 5.5% growth (₹155) because with RONIC > WACC, growth adds value.

Why is "value = PV of dividends" consistent with valuing a company that pays no dividends?

Answer

Retained cash either earns a return and funds larger future dividends/buybacks, or it is wasted. FCFF-based valuation captures the cash that *could* be paid; if management never pays it out and never earns a return on it, the value is genuinely lower — which the incremental-ROIC term already reflects.

Tapti Textiles is worth more not growing than growing at 6%. What should its management do, and what typically stops them?

Answer

Stop expanding, run for cash, return it (dividends/buybacks) or repay debt, and try to raise ROIC (pricing, cost, capital discipline) before growing again. What stops them: incentives tied to size, empire-building, the belief that scale will fix returns, and lenders/analysts who reward growth.

Go deeper¶

Tim Koller, Marc Goedhart & David Wessels (McKinsey), Valuation, chapters 2–3 — the value-driver formula and its proof; the whole book is the reference for this module.
John Burr Williams, The Theory of Investment Value (1938), chapter 5 — the original DCF.
Alfred Rappaport & Michael Mauboussin, Expectations Investing (2001; revised 2021) — price as forecast.
Warren Buffett, 1992 Berkshire letter — on why "growth" and "value" are joined at the hip.

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