Relative Valuation

Phase 3 · Week 31 · ~20 hours

Where it sits. Walk any trading floor, open any broker note, sit in any deal negotiation, and nobody says "my FCFF-to-firm value is ₹4.2 lakh crore"; they say "it's at 24 times forward" or "the deal printed at 15 times EBITDA." Roughly nine out of ten valuations done in practice are relative valuations. Sixth module of the valuation phase: the DCF modules before it built the intrinsic machine, meaning cash flows, discount rates, terminal values, and the reverse DCF that reads what a price implies. What follows is the other language, the one the market actually speaks. You must speak it fluently, and, more importantly, you must be one of the few speakers who knows what the words secretly mean, because every multiple is a compressed DCF: a discounted-cash-flow model where someone chose the assumptions, threw away the workings, and kept only the final ratio. Your edge is the ability to decompress it. On the five-questions spine (master map), this is question 5 again. What is the price implying, and is that beatable? Answered in minutes with a comps table instead of hours with a model, and cross-checked against the reverse DCF whenever the answer matters.

Suggested hour budget. Core content: 8h · worked examples: 2h · practice set: 5h · mini-project: 3h · flashcards + mastery check: 2h.

App link. The Relative Valuation branch runs on this material: the comps-builder in the valuation sandbox (assemble EV line by line from mock filings, graded per component), multiple-driver drill cards (given fundamentals, compute the justified multiple; given a multiple, back out the implied fundamental), "explain the gap" challenges (a comps table where every discount and premium must be attributed to a driver or flagged as residual), and the India-premium reverse-multiple challenges ("what growth for how long does 65× imply?").

Learning objectives

By the end you can:

1. Decompress any standard multiple into its drivers: derive and use justified P/E = payout × (1+g)/(r−g), P/B = (ROE−g)/(r−g), EV/EBITDA = (1−d)(1−t)(1−g/ROIC)/(WACC−g), EV/Sales = EBIT margin × (1−t)(1−g/ROIC)/(WACC−g), EV/IC = (ROIC−g)/(WACC−g), and P/FCFE = 1/(r−g), and state, for each multiple, the companion fundamental without which quoting it is meaningless.
2. Enforce the consistency grammar: pair equity multiples with equity (post-interest) numbers and enterprise multiples with all-capital (pre-interest) numbers; build EV correctly (market cap + debt + leases + minority interest + preferred − cash); spot and fix the EV/EPS and P/Sales sins in any table.
3. Choose true comparables by business model, not sector code, and normalize accounting before comparing: leases across ASC 842 / IFRS 16 / Ind AS 116, stock-based compensation, capitalized R&D/development, and one-offs, with the direction of each distortion memorized.
4. Aggregate a comp set defensibly: median and harmonic mean over arithmetic mean, outlier and loss-maker handling with the selection bias named, forward versus trailing chosen deliberately and never mixed.
5. Run a regression of multiples on fundamentals: fit the sector line (e.g., P/B against ROE for banks) by hand, price a firm off the line, and interpret the residual as a question rather than an answer.
6. Read precedent transactions and control premia: explain what a control premium pays for, where deal multiples come from (merger proxies, SEBI letters of offer), why they sit above trading multiples, and when applying them is a category error.
7. Apply India's premium-multiple discipline: explain the quality-scarcity / float / flows regime, prove with two-stage math what a 60–70× P/E requires (growth × duration × ROE), compute the multiple-drag on forward returns, and judge a premium multiple without either worshipping or dismissing it.
8. Build a full comps table end-to-end, one Indian sector and one US sector, from raw filings to a one-paragraph finding that attributes every premium and discount to a driver, and pass a timed comps workup graded against a key.

Prerequisites & connections

Builds on. M3.05 directly: the Gordon growth model is the engine under every justified multiple below, and the reverse DCF is the full-strength version of what "reversing a multiple" does in shorthand. M3.04: g = reinvestment rate × ROIC, the rule that links growth to reinvestment, reappears inside every enterprise-multiple formula as the (1−g/ROIC) term. M3.03: the r in every equity formula is that module's cost of equity, and the WACC in every EV formula is its WACC (we keep the sibling modules' illustrative mid-2026 anchors: US cost of equity ~8.5–9%, WACC ~8.5%; India cost of equity ~11.5–12%, WACC ~11.5%, check the live before real use). M2.01–M2.05: ROE, ROIC/ROCE, margins, and the benchmarking habit (normalize before comparing) are the fundamentals every multiple must be paired with. M1.08: lease accounting across the three standards, the biggest cross-border comps trap of all. M2.06–M2.07: one-off detection, because a comps denominator is only as good as your shenanigan filter.

Feeds forward. M3.07: EV/IC versus ROIC/WACC is the value-creation plot that module builds its capital-allocation verdicts on. M3.09: the comps and precedent-transaction tables you build here become two bars of the football field, built in a spreadsheet with full mechanics. M3.10: the phase capstone requires a three-way valuation (DCF, comps, reverse DCF) of one Indian and one US company, and the second leg is the one you build here. Phase 5 gives every sector its own multiple lens (P/B for banks, EV/EBITDAR for airlines, P/EV for life insurers). The grammar taught here is what makes those lenses safe to use. Phase 8's teardown question 11 ("what is the market implying?") is, nine times out of ten, answered by reversing a multiple the way you'll learn to here.

A multiple is a price divided by a fundamental, and it is cheap or expensive only relative to the drivers that justify it: growth, returns on capital, and risk. So the analyst's job is never to rank a column of numbers but to decompress each one and ask what it assumes.

Core teaching content

4.9 India's premium-multiple regime: and the growth-duration discipline

Put the two comps tables side by side and a puzzle appears. India's cost of equity is ~3 points higher than the US's, and the equity-multiple algebra says a higher r means lower justified multiples. The same stable business justifies ~13× forward in India against ~19× in the US. Yet look at the actual market. Nestlé India, Hindustan Unilever, Asian Paints, Pidilite, Titan have traded for years in the 50 to 80× trailing P/E region (check the current levels), while Nestlé S.A. trades near ~20× and P&G in the mid-20s. Indian quality trades at a large premium to identical-quality global peers, despite a 3-point rate handicap. Either the market is systematically mad, or something real is being priced. It's some of each, and your job is to measure which.

Three forces reinforce the premium:

1. Quality scarcity. Only a few dozen listed Indian businesses, in a market of thousands, combine durable 30%+ ROCE, clean governance, long reinvestment runways, and no promoter drama. Scarce quality gets a scarcity price, just as prime real estate does.
2. Float. The MNC parents hold ~62% of Nestlé India and ~62% of HUL (check the current shareholding patterns), and promoters hold similar or larger stakes elsewhere in the quality set. Free float, the part you can actually buy, is a fraction of market cap. Index inclusion forces passive money into that same fraction.
3. Flows. Domestic SIP inflows have compounded into a structural bid. Monthly SIP flows crossed roughly ₹26,000 crore during 2025 (check the current run-rate at amfiindia.com), and a disproportionate share of institutional mandates are quality-constrained. Persistent flows against limited float compress the effective discount rate the marginal buyer applies.

Look closely at what these forces are. Scarcity and flows are real, but they're price-setting conditions, and they aren't cash flows. A DCF can't see them, and a comps table can't see past them. So this regime needs its own method, and neither of the two lazy postures will do. One says "60× is a bubble, avoid", and that posture has kept skeptics out of two decades of compounding. The other says "quality always wins, price doesn't matter", and that one periodically loses investors a decade of returns.

Growth-duration math replaces both postures. A premium multiple is a claim about three numbers. There's the growth rate g, and the ROE that funds it. The third is the one amateurs skip: N, the number of years the growth phase lasts. The stable-growth ceiling proved that no steady state justifies 50×, so every 50×+ multiple is a statement about N. Make the statement explicit with the two-stage machinery from the terminal-value work:

P0 = Σ(t=1..N) [E0 × payout_h × (1+g_h)^t / (1+r)^t] + [E_N × (1+g_s) × payout_s / (r − g_s)] / (1+r)^N

Now work out what 65× trailing earnings requires. Take a Nestlé-India-like profile (illustrative). r = 11.5% (INR). High-growth ROE is 50%, so payout_h = 1 − g_h/50%. Terminal ROE is 30% and g_s = 5%, so payout_s = 0.833, and the terminal P/E from Gordon = 0.833 × 1.05/... It's simpler to fold the 1+g into the terminal earnings instead: TV_N = E_(N+1) × payout_s/(r − g_s).

Case A, a heroic decade and a half: g_h = 14% for N = 15 years, with payout at 72% throughout. Notice the luxury. At ROE 50%, even 14% growth retains only 28% of earnings.

• PV of dividends years 1–15: E0 × 0.72 × Σ(1.14/1.115)^t = 0.72 × 18.0 × E0 = 12.96 × E0
• E15 = E0 × 1.14^15 = 7.14 × E0; E16 = 7.50 × E0; TV15 = 7.50 × 0.833/0.065 = 96.1 × E0; PV = 96.1/1.115^15 = 96.1/5.118 = 18.78 × E0
• Justified trailing P/E = 12.96 + 18.78 ≈ 31.7×

Fifteen years of 14% compounding at 50% ROE is a run perhaps thirty listed companies on earth have delivered, and it justifies 32×, not 65×.

Case B, solve for what 65× actually needs: push to g_h = 16% for N = 25 years (payout 68%):

• PV of dividends: 0.68 × 43.54 × E0 = 29.6 × E0
• E25 = 40.9 × E0; TV25 = 40.9 × 1.05 × 0.833/0.065 = 550 × E0; PV = 550/15.20 = 36.2 × E0
• Justified trailing P/E ≈ 65.8×, a match for the market's multiple

So 65× is arithmetically sound, if and only if you underwrite 16% earnings growth sustained for twenty-five years at 50% ROE. Now bring in the outside view, which Phase 6 formalizes. In any market, the base rate of companies sustaining mid-teens earnings growth for 25 years is a low single-digit percentage. Mauboussin's Base Rate Book tabulates growth persistence, and the tails are thin. India's runway arguments (per-capita consumption at a fraction of developed levels, formalization, distribution depth) are real reasons to place an Indian name above the global base rate. They don't justify treating a 3-in-100 outcome as the central case for every quality name at once.

Even when the story is right, the entry multiple caps forward returns through multiple drag. Say earnings compound at 13% and the multiple drifts from 65× to 45× over a decade. Price CAGR = 1.13 × (45/65)^(1/10) − 1 = 8.9%, or about 9.9% with a ~1% dividend yield. That's below the 11.5% INR cost of equity, even though you owned a spectacular business that delivered 13% growth for ten straight years. With a flat multiple you'd earn ~14%, which is fine. Derate to 30× and it's 1.13 × (30/65)^(1/10) − 1 = 4.6%, plus yield ≈ 5.6%. That's a decade of world-class execution, turned into sub-FD returns by the entry price. Compound the drag, and don't subtract it. The shorthand answers of 13% − 3.6% and 13% − 7.4% drop the cross-term. They flatter the result by 0.47 points at 45× and by 0.97 points at 30×, and the gap widens with every turn of derating.

None of this is a bear argument. It's the return budget, stated plainly: at premium multiples your return is growth and yield net of multiple drag, and you control none of the three after purchase.

The premium-multiple checklist, for every name above 40×, Indian or otherwise:

1. Reverse the multiple. What (g, N, ROE) combinations justify today's price? It's a two-stage calculation and takes five minutes.
2. Base-rate the claim. How many companies anywhere have delivered that combination? Does this one have structural reasons to beat the odds?
3. Put a number on the flow and float component. How much of the multiple is scarcity pricing that new supply (IPOs of peers, promoter stake sales, MNC delistings reversing) or a reversal of flows could remove?
4. Budget the drag. Compute expected return under flat / modest-derate / harsh-derate multiples. Would you still own it in the middle case?
5. Watch the growth-multiple covenant. Premium names are priced for never missing, so track volume growth. Phase 5's FMCG rule applies here: value growth on flat volumes is borrowed time. And keep in mind that the exit door is narrow when float is thin, in both directions.

So that's what "respect India's premium-multiple regime" means. You don't defer to the multiple and you don't deride it. You decompress it, base-rate it and budget the return.

Common mistakes & how experts think differently

1. Quoting a multiple without its companion fundamental. "It's at 14×" tells you nothing. "14× at what ROE, what growth, what leverage" does. Experts speak in pairs, as in "14× for a 10% ROCE", because a multiple alone is a numerator shopping for a story. The amateur ranks the multiple column. The expert reads the driver columns and asks what the multiple column should look like.

2. The grammar sins: EV/EPS and P/Sales. Crossing claim levels produces numbers that move when the CFO refinances and nobody's operations change. Experts run the claim-level check on every inherited table before reading a single row, and they end up re-ranking half of them.

3. Comparing across accounting regimes without normalizing. Lease-fat Ind AS EBITDA gets set against rent-burdened US GAAP EBITDA. SBC-excluding "adjusted" figures get set against GAAP, and R&D capitalizers against expensers. Each error has a known direction, and in every case the flattered side looks cheap: non-US names, adjusted figures, capitalizers. Experts memorize the directions and sense a wrong table before they can prove it.

4. Trailing P/E on cyclicals and turnarounds. A cyclical's P/E is lowest at the earnings peak, which is a sell signal misread as a bargain. It's highest at the trough, a buy zone misread as expensive. A turnaround shows the same artifact through a depressed denominator, as Tech Mahindra did in the IT table. Experts normalize the denominator (mid-cycle earnings, recovered margins) before computing anything.

5. Arithmetic means over unexamined sets. One 60× glamour name drags the "peer average" up four turns. Loss-makers vanish from P/E medians without a word, and a non-comparable slips into the set because the sector code said so. Experts use the median plus the harmonic mean, name every exclusion, and treat a mean/median divergence as a smoke alarm.

6. PEG worship. Reading PEG < 1 as "cheap" fails the derivation you did for P/E. P/E isn't linear in g, it isn't zero at g = 0, and PEG ignores r and ROE. Experts use PEG, if ever, as a rough same-risk screen and never as evidence.

7. Relative cheapness in an absolutely expensive group. "Cheapest large-cap SaaS name" in 2021 was still 15× sales. A comps table can only rank the room. It can't tell you the room is on fire. Experts anchor every relative verdict to one absolute check, either the reverse DCF or the stable-growth ceiling (1/(r−g)).

8. Paying control prices for minority claims. Precedent-transaction multiples embed control value and synergies, plus the winner's curse. Apply them to a 100-share purchase and you import a premium you'll never be able to exercise. The mirror error is valuing a real acquisition off trading comps and then wondering why every bid loses.

9. Treating the sector regression as an answer. The fitted line describes today's pricing. A residual below the line is a question: what does the market see that my two regressors don't? Experts investigate residuals. Amateurs buy them.

10. Dismissing or worshipping India's premium multiples. "60× is absurd" and "quality is priceless" are the same mistake, a refusal to do the two-stage arithmetic. Experts decompress the multiple into (g, N, ROE), base-rate it, separate the flow/float component, and budget the multiple drag before forming a view.

Amateurs use multiples to avoid doing a DCF. Experts use them as a compressed, reversible DCF, a way to read the market's assumptions in seconds and disagree with them on evidence. They also know which assumption the disagreement is about. Same tool, opposite direction of information flow.

Worked examples

Worked example 1: One firm, every equity multiple (and the inversion)

Saraswati Consumer Ltd (synthetic Indian FMCG): ROE 24%, stable growth 6%, cost of equity 11.5%, current EPS ₹20, book value per share ₹83.3 (so that ROE × BV = 24% × 83.3 = ₹20, which checks), market price ₹600.

Step 1: justified multiples. Payout = 1 − g/ROE = 1 − 6/24 = 0.75.

• Forward P/E = 0.75/(0.115 − 0.06) = 0.75/0.055 = 13.6×
• Trailing P/E = 0.75 × 1.06/0.055 = 14.5×
• P/B = (ROE − g)/(r − g) = (24 − 6)/(11.5 − 6) = 18/5.5 = 3.27×
• Cross-check via the identity: P/B = ROE × forward P/E = 0.24 × 13.6 = 3.27×, the same answer

Step 2: value and verdict. Justified price = trailing P/E × EPS = 14.5 × 20 = ₹289, against a market price of ₹600. That's a wide gap. At the market price the stock is on trailing 30× and P/B 600/83.3 = 7.2×. The market is pricing something far beyond the stable state.

Step 3: invert the multiple (the five-minute reverse DCF). What perpetual growth would justify 30× trailing, holding ROE 24% and r 11.5%? Solve (1 − g/0.24)(1+g)/(0.115 − g) = 30 by trial. At g = 9%: (0.625)(1.09)/0.025 = 27.3×. At g = 9.5%: (0.604)(1.095)/0.02 = 33.1×. So g ≈ 9.3% fits. A 9.3% forever growth rate breaches the terminal cap by a distance. The terminal-value rule sets that cap at the risk-free rate in your own stack. On the credit-cleaned rupee build from the cost-of-capital work (a 6.5% G-sec less a 2.0-point sovereign default spread), that's 4.5%, or 6.5% if you keep the raw G-sec and use it consistently in both places. India's ~10 to 11 percent nominal GDP growth isn't the test. That's today's economy, and a perpetuity describes the mature one. So the price only makes sense as a high-growth-phase claim, for example ~12 to 13% for 15 years and then 5%. You can check that with the two-stage machinery from the India section. The comps question has become a falsifiable forecast question, and turning it into one is what driver algebra is for.

Worked example 2: One firm, every enterprise multiple (four shirts, one value)

Deccan Precision Ltd (synthetic Indian components maker), next-year figures: revenue ₹4,200 crore, EBITDA ₹1,050 crore (25% margin), D&A ₹315 crore (d = 0.30), EBIT ₹735 crore (17.5% margin). Tax at 25% leaves NOPAT of ₹551 crore. Invested capital today is ₹3,675 crore, so forward ROIC = 551/3,675 = 15%. Growth g = 5% and WACC = 11%.

Step 1: value once. Reinvestment rate = g/ROIC = 5/15 = 1/3. FCFF1 = 551 × (1 − 1/3) = ₹367.5 crore. EV = 367.5/(0.11 − 0.05) = ₹6,125 crore.

Step 2: read the same value through four multiples. Verify each one against its driver formula:

One DCF, four denominators. The four multiples are one value wearing four shirts. If a real company's four multiples imply different values against peers, the disagreement is itself information, and usually it points to an accounting artifact in one denominator.

Step 3: the capex-intensity twist. A peer, Konkan Heavy Forgings, has identical growth, tax and ROIC, but d = 0.55 because its machinery is heavy and long-lived. Its justified EV/EBITDA = (0.45)(0.75)(2/3)/0.06 = 3.75×. Both firms now trade in the market at 4.8× EV/EBITDA. So Deccan (justified 5.8×) is ~17% cheap, and Konkan (justified 3.75×) is ~28% dear, at the same headline multiple. "Cheap on EBITDA" without d is a coin flip.

Worked example 3: Cross-border normalization: leases + SBC in one table

You're comparing Bluegrass Stores (US, ASC 842) with Kaveri Retail (India, Ind AS 116). Here's the raw data:

The naive table, which is what vendor screens do: Bluegrass EV = 16,000, so EV/adj EBITDA = 16,000/2,150 = 7.4×. Kaveri EV = 15,500, so EV/EBITDA = 15,500/2,500 = 6.2×. Conclusion: "Kaveri 16% cheaper." Both numbers are wrong, in three ways (lease convention differs, SBC treatment differs, lease debt inconsistently included).

The clean, lease-inclusive, SBC-expensed table:

• Bluegrass: EBITDA pre-rent, SBC-expensed = 2,000 + 300 = $2,300m, and EV = 16,000 + 2,400 = $18,400m, which gives 8.0×
• Kaveri: EBITDA already pre-rent = ₹2,500 cr, and EV = 15,000 + 500 + 4,000 = ₹19,500 cr, which gives 7.8×

Put them on the same convention and the two retailers price within 2 to 3% of each other. The "16% discount" was accounting, and there was no opportunity in it. Now a direction drill. Which way would each uncorrected error move a real decision? The naive treatment made the Ind AS 116 firm look cheap, the standing direction from the lease rules. And the SBC add-back made the US firm look cheap on its "adjusted" line. Two flattering errors pointing opposite ways are why raw cross-border tables are noise.

Worked example 4: Precedent transactions and the control-premium budget

Meridian Foods Ltd (synthetic Indian packaged-foods target): revenue ₹2,400 crore, EBITDA ₹360 crore (15% margin), net debt ₹200 crore, 10 crore shares. At the unaffected market price of ₹680, market cap is ₹6,800 crore and EV is ₹7,000 crore, so it trades at 19.4× EV/EBITDA.

Step 1: assemble precedents. These are illustrative control deals in Indian F&B, screened on the precedent rules above: strategic buyers, cash-heavy consideration, last 4 years.

Step 2: indicated control value. EV at 24 to 28× (the inter-quartile band around the median) = ₹8,640 to 10,080 crore. Equity = EV − net debt = ₹8,440 to 9,880 crore, or ₹844 to 988 per share. The midpoint is ~₹916, a 35% premium to the unaffected ₹680. That's square in the historical 25 to 40% control-premium band, which is your consistency check that the precedent set and the premium evidence agree.

Step 3: the buyer's budget. Now do the acquirer's own homework. Standalone DCF value is ₹720/share and the PV of credible synergies is ₹150/share, so the maximum rational price is ₹870. The precedent median says ₹916. The gap is the market's history of winner's curse, with at least one prior buyer in the table paying for synergies it never got. The buyer's rule is to bid up to your ₹870 ceiling and walk above it. Let the precedent table shape the seller's expectations and leave your own alone. The seller's rule is that the table is your negotiating floor. And the minority investor's rule is that none of these numbers is yours. You're buying at ₹680 without control, so the 26× matters only as an eventual exit scenario with a probability attached. It's never "fair value."

Worked example 5: Building enterprise value from a cap table (US $)

Cascade Industrial Corp (synthetic US mid-cap): the market quotes only the equity, but every enterprise multiple needs the whole enterprise. So assemble it line by line from the capital structure. It's the same skill the app's comps-builder grades per component.

Step 1: diluted market cap (treasury stock method). The share price is $48.00, with 200.0m basic shares, plus 12.0m in-the-money employee options struck at $30.00. Options are claims that exist today, so dilute. Assumed exercise raises 12.0 × $30 = $360m, which buys back 360/48 = 7.5m shares at the current price and leaves 4.5m net new shares. Diluted shares = 204.5m, and diluted market cap = 204.5 × $48 = $9,816m. Basic shares would understate the numerator, and that's the first of four ways this build goes wrong.

Step 2: add the non-equity capital claims, and subtract what the buyer gets back. Each line is either a claim on the operations or something the buyer receives, and the last column says which.

Step 3: pair EV with a lease-consistent denominator. Reported EBITDA (ASC 842) is $1,850m, with $120m of operating-lease rent inside it as expense. EV is lease-inclusive, since we added the $700m lease liability, so the denominator must be pre-rent. Add the rent back and you get $1,970m. Forward EV/EBITDA = 12,666/1,970 = 6.43×. Total D&A, including right-of-use depreciation, is $340m, so EBIT = 1,970 − 340 = $1,630m and EV/EBIT = 7.77×.

Step 4: feel how each shortcut lies. Use basic shares instead of diluted and EV falls to $12,450m, or 6.32×, which is too cheap. Forget to subtract the non-operating stake and EV is $13,266m, or 6.73×, which is too dear. Pair lease-inclusive EV with the reported rent-in EBITDA and you get 12,666/1,850 = 6.85×, a fake premium from a convention mismatch. Three errors, three directions. So build every line, and never inherit an EV blind.

Worked example 6: Decompressing a premium P/E: single-stage, two-stage, and the return budget (India ₹)

Vindhya Consumer Ltd (synthetic Indian FMCG): ROE 40%, cost of equity 11.5%, terminal growth 5%, current EPS ₹30, market price ₹1,350.

Step 1: the single-stage justified multiple. Payout = 1 − g/ROE = 1 − 5/40 = 0.875. A capital-light 40%-ROE firm funds 5% growth and still pays out seven-eighths of its earnings. Forward P/E = 0.875/(0.115 − 0.05) = 13.46×, and trailing = 0.875 × 1.05/0.065 = 14.13×. So a steady-state Vindhya is worth 14.13 × ₹30 = ₹424.

Step 2: the market's number, and the gap. The stock trades at ₹1,350 = 45× trailing, more than three times the steady-state fair value. The stable-growth ceiling says 1/(r−g) = 1/0.065 ≈ 15.4× even at infinite ROE, so 45× can't be a steady-state price. It's a claim about a high-growth phase. Name the claim with the two-stage machinery.

Step 3, two-stage: what does 45× require? In the terminal stage, ROE is 30% and g is 5%, so payout_s = 1 − 5/30 = 0.833. Now solve for the high-growth rate g_h and the duration N, with ROE at 40% throughout the phase, that reproduce 45× trailing:

• Case A, heroic but bounded: g_h = 14% for N = 25 years gives a justified trailing P/E of 45.4×, which matches. Twenty-five years of 14% earnings compounding at a 40% ROE is a run only a handful of companies in history have delivered, and it's what the price underwrites.
• Case B, merely excellent: g_h = 12% for N = 15 years justifies only 25.3×. The distance from 25× to 45× is the market's bet on the extra decade-plus of high growth.

Step 4: base-rate the claim and budget the return. The base rate of firms sustaining mid-teens earnings growth for 25 years is low single digits (Mauboussin's Base Rate Book). India's runway may lift Vindhya above the global base rate, but it doesn't make a 3-in-100 outcome the central case. And even if the story is right, the entry multiple caps the return through multiple drag. Buy at 45×, let EPS compound at 14% for a decade, and add a ~1.4% dividend yield:

So a flawless 14% compounder bought at 45× returns below the 11.5% cost of equity once the multiple merely drifts toward its steady-state ceiling. That's the growth-duration method in one worked case. Decompress the multiple, base-rate the claim, budget the drag. Then decide.

Practice set

The set ramps up. P1 to P3 are guided single-formula drills, P4 to P8 are multi-step applications, and P9 to P11 are independent and timed. Unless stated otherwise, use these illustrative anchors: India cost of equity 11.5 to 12%, WACC 11 to 11.5%; US cost of equity 8.5 to 9%, WACC 8.5 to 9%; tax 25% in both markets. In real work, use live inputs, always.

P1 (guided). A firm has ROE 20%, stable growth 5%, cost of equity 10%. Compute (a) the payout ratio, (b) the justified forward P/E, (c) the justified trailing P/E.

Solution. (a) Payout = 1 − g/ROE = 1 − 5/20 = 0.75. (b) Forward P/E = 0.75/(0.10 − 0.05) = 15.0×. (c) Trailing = 0.75 × 1.05/0.05 = 15.75×.

P2 (guided). Two banks, both with cost of equity 12% and stable growth 6%. Bank X earns ROE 22% and Bank Y earns ROE 10%. (a) Justified P/B for each. (b) One sentence: what does growth do to Y's multiple, and why?

Solution. (a) X: (22 − 6)/(12 − 6) = 16/6 = 2.67×. Y: (10 − 6)/(12 − 6) = 4/6 = 0.67×. (b) Growth lowers Y's P/B further, to 3/5 = 0.60× if g rises to 7%, because a bank earning below its cost of equity destroys value with every rupee of book it adds, so faster growth means faster destruction.

P3 (guided: grammar audit). An intern's table contains: (i) "EV/EPS: 18×", (ii) "P/EBITDA: 6×", (iii) "Company A (net debt 3× EBITDA) at 0.5× P/S is cheaper than Company B (net cash) at 0.8× P/S." Identify each error and state the fix.

Solution. (i) The EV/EPS sin. It's an all-capital numerator over an equity-only denominator, so refinancing changes the ratio with no operating change. Fix: EV/EBIT(DA) or P/E. (ii) The same sin mirrored, an equity numerator over a pre-interest denominator, which makes a levered firm look artificially cheap. Fix: EV/EBITDA. (iii) P/S is inconsistent, equity over all-claim revenue, so A's debt is invisible in the ratio. Fix: EV/Sales. A's EV includes the debt and will likely show dearer than B, which reverses the conclusion.

P4. A US logistics firm: D&A is 35% of EBITDA, tax 25%, ROIC 18%, stable growth 4.5%, WACC 9%. (a) Justified forward EV/EBITDA. (b) Recompute for a peer identical except ROIC = 9%. (c) One sentence on the comparison.

Solution. (a) Reinvestment factor = 1 − 4.5/18 = 0.75. EV/EBITDA = 0.65 × 0.75 × 0.75/0.045 = 0.3656/0.045 = 8.1×. (b) Factor = 1 − 4.5/9 = 0.50, so 0.65 × 0.75 × 0.50/0.045 = 5.4×. (c) Same EBITDA and same growth, yet the ROIC = WACC peer deserves ~33% less per unit of EBITDA, because its growth consumes twice the capital and creates none of the value, so if the two trade at the same multiple, the high-ROIC firm is the cheap one.

P5. A listed foodtech platform trades at 6× EV/Sales. Assume it matures to WACC 9.5%, stable growth 4%, light reinvestment (1 − g/ROIC = 0.85), tax 25%. (a) What steady-state EBIT margin is the price implying? (b) The best listed food-service margins run ~20 to 25%. Verdict?

Solution. (a) 6 = m × 0.75 × 0.85/(0.095 − 0.04), so m = 6 × 0.055/0.6375 = 51.8%. (b) The price implies more than double the best-ever mature margin for the business model, so today's 6× is not a steady-state price. It needs years of hyper-growth first. Either underwrite that growth phase explicitly with a two-stage model, or pass. "6× is normal for platforms" isn't an argument.

P6. Four firms are all fairly priced with ROE 18% and r 9%: their stable growth rates are 2%, 4%, 6%, 8%. (a) Compute each justified forward P/E and each PEG. (b) Which does PEG call cheapest, and what is the correct statement?

Solution. (a) Payouts: 0.889, 0.778, 0.667, 0.556. P/Es: 0.889/0.07 = 12.7×, 0.778/0.05 = 15.6×, 0.667/0.03 = 22.2×, 0.556/0.01 = 55.6×. PEGs: 12.7/2 = 6.35, 15.6/4 = 3.89, 22.2/6 = 3.70, 55.6/8 = 6.94. (b) PEG anoints the 6% grower (3.70), but all four are at fair value by construction. The correct statement is that PEG isn't comparable even across correctly priced firms, because P/E is convex in g and has a value floor at g = 0. Ranking on PEG manufactures conclusions from curvature.

P7. Peer P/Es: 12, 18, 22, 30, 95 (the 95× is a turnaround with depressed earnings). A sixth peer is loss-making. Compute the mean, median, and harmonic mean of the five. Then state how to handle peers five and six.

Solution. Mean = 177/5 = 35.4×. Median = 22×. Harmonic = 5/(1/12 + 1/18 + 1/22 + 1/30 + 1/95) = 5/0.2282 = 21.9×. Handling: the 95× is a depressed-denominator artifact, so either normalize its earnings before inclusion or exclude it with a stated reason. Notice how the median and harmonic mean barely feel it while the mean is wrecked. The loss-maker can't enter a P/E aggregate at all, so name the exclusion. If loss-makers are a large fraction of the sector, switch the whole comparison to EV/EBITDA or EV/Sales to avoid the survivor-optimism bias.

P8. A US restaurant chain (ASC 842): reported EBITDA $1,200m with rent of $300m inside it as expense, market cap $9,000m, debt ex-leases $600m, lease liabilities $2,400m. An Indian QSR (Ind AS 116): reported EBITDA ₹900 crore (rent of ₹200 crore already relocated below EBITDA), market cap ₹6,000 crore, borrowings net of cash ₹400 crore, lease liabilities ₹1,600 crore. (a) Compute the naive comparison an unadjusted screen would show (lease-exclusive EV over reported EBITDA). (b) Compute both on a consistent lease-inclusive basis. (c) Verdict.

Solution. (a) US: EV = 9,000 + 600 = 9,600, and 9,600/1,200 = 8.0×. India: EV = 6,000 + 400 = 6,400, and 6,400/900 = 7.1×. The screen says "the Indian chain is 11% cheaper." (b) Lease-inclusive: US EBITDA pre-rent = 1,200 + 300 = 1,500, and EV = 9,600 + 2,400 = 12,000, so 8.0×. India: EBITDA is already pre-rent at 900, and EV = 6,400 + 1,600 = 8,000, so 8.9×. (c) Measured consistently, the Indian chain is ~11% dearer. The naive screen had the sign wrong, because Ind AS 116 fattens EBITDA while the screen ignored the matching lease debt. The US multiple comes out at 8.0× on both bases only because of these particular numbers, with rent capitalized at 8× on the nose. That isn't a general rule, so run both bases every time.

P9. Five specialty chemical firms: ROIC (x) = 8, 12, 16, 20, 24 (%); forward EV/EBITDA (y) = 6.0, 8.0, 10.5, 12.0, 13.5. (a) Fit y = a + bx by OLS (show Sxy, Sxx). (b) A sixth firm has ROIC 18% and trades at 9.0×; compute its regression-fair multiple and residual. (c) Two sentences of correct interpretation.

Solution. (a) x̄ = 16 and ȳ = 10.0. Deviations: x: −8, −4, 0, 4, 8; y: −4, −2, 0.5, 2, 3.5. Sxy = 32 + 8 + 0 + 8 + 28 = 76, and Sxx = 64 + 16 + 0 + 16 + 64 = 160. b = 76/160 = 0.475 and a = 10 − 0.475×16 = 2.4. Line: EV/EBITDA ≈ 2.4 + 0.475 × ROIC. (b) Fair = 2.4 + 0.475×18 = 10.95×, and the residual = 9.0 − 10.95 = −1.95, which is ~18% below the line. (c) The firm is cheap relative to how the sector currently prices ROIC, which is either a mispricing or a sign that the market doubts the 18% ROIC's durability (accounting quality, cyclicality, reinvestment cliff). The regression locates the question, and the Phase 2 toolkit answers it.

P10. Four control deals in a sector closed at premia of 22%, 29%, 31%, 38% over unaffected prices. Your target's unaffected price is ₹460. Your standalone DCF says ₹520, and your synergy PV is ₹40/share. (a) Median-premium indicated offer. (b) The buyer's maximum rational bid. (c) Reconcile in two sentences.

Solution. (a) Median premium = (29 + 31)/2 = 30%, so the indicated offer = 460 × 1.30 = ₹598. (b) Max rational = 520 + 40 = ₹560. (c) Precedents say the market has paid ~₹598 for control of similar assets, but ₹38 of that is value the average past buyer hoped for and, statistically, overpaid for, which is the winner's curse embedded in every precedent table. Bid to your ₹560 ceiling, and if the auction clears higher, losing is winning.

P11 (timed: 25 minutes, no notes). Five synthetic Indian pharma firms (₹ crore). WACC ≈ 11.5%.

Compute EV/EBITDA and P/E for all five, the sector median EV/EBITDA, and write a five-line reading: who is cheap-for-a-reason, who is the residual anomaly, and what one question you would research next.

Solution. EVs: V 42,000, W 24,000, X 22,000, Y 31,000, Z 12,500. EV/EBITDA: V 14.0×, W 15.0×, X 11.0×, Y 14.1×, Z 13.9×. P/E: V 22.2×, W 25.0×, X 20.0×, Y 22.2×, Z 23.1×. Median EV/EBITDA = 14.0× (11.0, 13.9, 14.0, 14.1, 15.0). Reading: X is cheap-for-a-reason. It has the slowest growth (5%), ROCE ≈ WACC (11% vs 11.5%, so no value creation), and the most levered book (net debt 2× EBITDA). Its 21% discount to median is the market correctly charging for all three. Z is the residual anomaly. Its growth (12%) and ROCE (21%) are almost the same as W's, yet Z trades at 13.9× against W's 15.0×, and below the sector median despite above-median fundamentals. V and Y price in line with their drivers. The next question is why Z trades at W's fundamentals minus one turn. Is it a size or liquidity discount (₹12,000 crore cap), promoter overhang or pledge, a one-off in the EBITDA base, or a real mispricing? Pull the shareholding pattern and the exceptional-items note first, using the benchmarking and shenanigans toolkits.

P12 (guided: EV build). Sahyadri Foods (synthetic): diluted market cap ₹8,000 crore; total borrowings ₹1,500 crore; lease liabilities ₹900 crore; minority interest ₹300 crore; preferred nil; cash and liquid investments ₹1,200 crore; a listed non-operating associate (equity-method, so its profit is booked below EBIT and stays out of EBITDA) worth ₹700 crore. Pre-rent, lease-inclusive EBITDA is ₹1,400 crore. (a) Build EV. (b) EV/EBITDA. (c) An analyst forgets both the minority interest and the non-operating stake. What EV/EBITDA results, and why is "the errors cancel" a dangerous hope?

Solution. (a) EV = 8,000 + 1,500 + 900 + 300 + 0 − 1,200 − 700 = ₹8,800 crore. (b) 8,800/1,400 = 6.29×. (c) Omitting minority interest drops ₹300 crore. Failing to subtract the stake leaves ₹700 crore in. So EV = ₹9,200 crore and 9,200/1,400 = 6.57×, about 4.5% too dear. The two errors point opposite ways but are unequal, so they don't cancel. Relying on offsetting mistakes is how a wrong number survives review. Build every line.

P13 (guided: the owner's multiple). A mature US cash generator produces forward FCFE of $1.2bn; cost of equity 9%, stable growth 4%; it trades at a market cap of $26bn. (a) Justified forward P/FCFE and justified market cap. (b) Current FCFE yield and the fast "FCF yield + g" expected-return check. (c) Cheap or dear?

Solution. (a) Forward P/FCFE = 1/(r − g) = 1/0.05 = 20.0×. There's no payout term, because FCFE is already post-reinvestment. Justified market cap = 20 × 1.2 = $24bn. (b) FCFE yield = 1.2/26 = 4.62%, and expected return ≈ yield + g = 4.62% + 4% = 8.62%. (c) It trades at 26/1.2 = 21.7×, above the 20× justified, and the 8.62% implied return is below the 9% cost of equity, so it's mildly dear. One trap to avoid: putting a payout ratio into the P/FCFE formula double-counts reinvestment.

P14. Three synthetic Indian capital-goods firms; WACC 11.5%, all with stable growth 5%.

(a) Compute each firm's justified EV/IC. (b) Place each above / on / below the value-creation line and state the research question its residual raises.

Solution. (a) EV/IC = (ROIC − g)/(WACC − g), with WACC − g = 6.5. A: (25 − 5)/6.5 = 3.08×. B: (14 − 5)/6.5 = 1.38×. C: (11 − 5)/6.5 = 0.92×. (b) A, at 2.6× against 3.08× justified, is ~16% below the line. So it's cheap, or the market doubts the durability of its 25% ROIC (reinvestment cliff, competitive fade), which is a Phase 2 durability question. B, at 1.4× against 1.38×, is essentially on the line, fairly priced for a modest positive spread. C, at 1.3× against 0.92×, is above the line even though its ROIC (11%) is below WACC (11.5%). The market is paying more than a rupee per rupee of capital for a marginal value-destroyer. It's betting the ROIC recovers above WACC, which is the only thing that would justify the premium. Every dot off the line is a question, never a verdict.

P15. An Indian compounder trades at 48× trailing earnings. Its cost of equity is 11.5% and its high-growth-phase ROE is 45%. Terminal ROE is 28%, with terminal growth of 5%. Assume a high-growth phase of N = 20 years. (a) Compute the justified trailing P/E at g_h = 12% and g_h = 14%. (b) Roughly what constant g_h would justify today's 48×? (c) One sentence on the base-rate check.

Solution. (a) Terminal payout = 1 − 5/28 = 0.821, and the phase payout = 1 − g_h/0.45. Run the two-stage model, discounted at 11.5%. At g_h = 12% it gives 29.9×, and at g_h = 14% it gives 38.2×. (b) 48× is above both, so it needs g_h ≈ 15.8% sustained for the full 20 years, or 14% over a still-longer runway. (c) A 15 to 16% earnings CAGR held for two decades is a low-single-digit-percent base-rate event (Mauboussin), so 48× is neither "expensive" nor "cheap" until you judge whether this firm has structural reasons to beat those odds. The multiple has become a falsifiable forecast.

P16. You buy a US quality compounder at 42× trailing earnings. Over the next decade EPS compounds at 12% and the dividend yield averages ~0.8%. Compute the total expected annual return under three exit multiples: (a) flat at 42×, (b) a derate to 30×, (c) a derate to 22×.

Solution. Total return ≈ (1 + g_EPS) × (exit/entry)^(1/N) − 1 + yield. (a) Flat: 1.12 × 1 − 1 = 12.0% + 0.8% = 12.8%. (b) 30×: 1.12 × (30/42)^(1/10) − 1 = 1.12 × 0.9669 − 1 = 8.29%, plus 0.8% = 9.1%, with multiple drag ≈ −3.3%/yr. (c) 22×: 1.12 × (22/42)^(1/10) − 1 = 4.99%, plus 0.8% = 5.8%, with drag ≈ −6.3%/yr. The business quality is identical across the three columns. The entry multiple decides whether a superb decade pays 12.8% or 5.8%, and the earnings don't. After purchase you control none of growth, yield, or derating.

P17 (timed: 20 minutes, no notes). Compare two synthetic pure-play retailers. Ignore FX, and judge each on its own consistently measured multiple.

(a) Compute the naive comparison a vendor screen shows: lease-exclusive EV over each firm's headline EBITDA (reported for Nilgiri, "adjusted" for Summit). (b) Recompute both on a consistent lease-inclusive, SBC-expensed basis. (c) Which retailer is really cheaper, and by how much? Name the two errors that flipped the naive answer.

Solution. (a) Naive: Nilgiri EV = 20,000 + 800 = 20,800, and 20,800/3,000 = 6.93×. Summit EV = 18,000 + 500 = 18,500, and 18,500/2,600 = 7.12×. The screen says Nilgiri is cheaper. (b) Clean: Nilgiri's EBITDA is already pre-rent and SBC-free at 3,000, and EV = 20,000 + 800 + 5,000 = 25,800, so 8.60×. Summit's pre-rent, SBC-expensed EBITDA = 2,400 + 400 rent = 2,800, rejecting the SBC add-back. Its EV = 18,000 + 500 + 3,000 = 21,500, so 7.68×. (c) Summit is really cheaper, 7.68× against 8.60×, or about 11% cheaper, which reverses the naive verdict. Two flattering errors did it. Ind AS 116 fattens Nilgiri's EBITDA while the naive EV omits its ₹5,000 crore lease liability, the standing direction that non-US looks cheap. And accepting Summit's SBC add-back inflated its denominator (making the US name look dear). Currency didn't decide the ranking. Consistency did.

P18. (independent) A cash multiple, cleaned, and a screen that is not a multiple (India). Deccan Agri Foods (synthetic): enterprise value ₹5,000 crore; cash from operations ₹500 crore; interest paid ₹80 crore; tax rate 25%; capital expenditure ₹240 crore; net income ₹300 crore; depreciation and amortization ₹190 crore; 100 crore diluted shares; market capitalization ₹4,200 crore. The same screen also reports that last quarter's earnings came in at ₹13.10 against a ₹12.40 consensus, and that the standard deviation of this company's past surprises is ₹0.28. (a) Compute EV/CFO as the screen reports it and EV/unlevered-CFO as the grammar requires, and say which peer in a table the error would flatter most. (b) Compute P/CF on cash earnings and P/FCFE, and say what the gap between them is measuring. (c) Compute the standardised unexpected earnings, and state in one sentence what it does and does not entitle you to conclude.

Solution. (a) Naive EV/CFO = 5,000/500 = **10.0×**. Unlevered CFO = 500 + 80 × (1 − 0.25) = ₹560 crore, so the matched multiple is 5,000/560 = **8.93×**. The naive figure overstates by 12.0%, and it overstates most for the most levered peer, because the more interest a company pays, the more of its operating cash has already left before CFO is struck. In a screen sorted on EV/CFO, the leveraged names look expensive and the debt-free ones look cheap, purely as an artifact of the mismatch. (b) Cash earnings per share = (300 + 190)/100 = ₹4.90; price = 4,200/100 = ₹42; P/CF = 42/4.90 = **8.57×**. FCFE per share = (500 − 240)/100 = ₹2.60; P/FCFE = 42/2.60 = **16.15×**. The gap is the capital intensity of the business: ₹2.40 a share of capex that P/CF does not charge for and the owner does. (c) UE = 13.10 − 12.40 = +₹0.70; SUE = 0.70/0.28 = **+2.5**. That's a large positive surprise by this company's own history, and the evidence on post-earnings-announcement drift says such surprises tend to be followed by further positive drift over the next few months. It says nothing whatever about whether 8.93× is a fair price for the enterprise. A momentum signal and a valuation conclusion are different claims, and the table should keep them in different columns.

Applied mini-project

Task: two live comps tables, one Indian sector and one US sector, built end-to-end, with a regression and a one-page finding. Pick one Indian set and one US set. Recommended Indian sets: IT services (TCS, Infosys, HCLTech, Wipro, Tech Mahindra, LTIMindtree) or paints (Asian Paints, Berger, Kansai Nerolac, Akzo Nobel India, Indigo Paints). Recommended US sets: beverages (KO, PEP, KDP, Monster, Celsius) or home improvement (Home Depot, Lowe's, Floor & Decor, Tractor Supply). They're teaching specimens, and none of them is a recommendation. Data: annual reports / 10-Ks (BSE/NSE company pages, SEC EDGAR), screener.in for Indian financials, stockanalysis.com or TIKR (free tiers) for US financials and consensus forward estimates. Deliver a spreadsheet plus a one-page memo:

1. Universe page: every name admitted or rejected, with the business-model reason in one line each.
2. EV build: market cap (diluted), debt, lease liabilities (cite the note number), minority interest, preferred, cash and liquid investments, non-operating stakes. One lease convention for the whole table, stated at the top.
3. Denominator hygiene log: every adjustment made (one-offs, SBC, capitalized development, associates), with direction of effect.
4. The table: trailing and forward blocks; fundamentals columns (growth, EBIT margin, ROCE/ROIC or ROE, net debt/EBITDA); median + harmonic aggregates; outliers flagged.
5. One regression: the sector's natural pairing (P/B on ROE if you chose banks-like economics; EV/EBIT or EV/EBITDA on ROCE/ROIC otherwise; P/E on forward growth acceptable). Report slope, intercept, R², and each firm's residual.
6. The finding: one page. Attribute every material premium or discount to a driver. Name the single residual anomaly most worth researching and the one question you'd answer next. State explicitly what this table cannot tell you, which is the absolute-level caveat. And cross-check one name against a quick reverse-multiple: what g for how long does its multiple imply?

Scoring rubric (pass ≥ 80% of available points; log score and top miss in the journal):

Reading & resources

Primary texts.

• Aswath Damodaran, Investment Valuation (3e), Ch. 17 (Fundamental Principles of Relative Valuation), Ch. 18 (Earnings Multiples), Ch. 19 (Book Value Multiples), Ch. 20 (Revenue Multiples and Sector-Specific Multiples): the driver algebra at full depth, including the regression approach. [Paid] [Intermediate]
• Damodaran, The Little Book of Valuation: the relative-valuation chapters for a fast second pass. [Paid] [Beginner]
• McKinsey (Koller, Goedhart, Wessels), Valuation (8e, 2025), the "Valuation by Multiples" chapter: the practitioner-house method (forward multiples, EV/EBITA, peer selection); note where it differs from Damodaran (EBITA emphasis, tighter peer sets) and why both are defensible. [Paid] [Intermediate]
• Rosenbaum & Pearl, Investment Banking, Ch. 1 (Comparable Companies Analysis) and Ch. 2 (Precedent Transactions Analysis): the banker's mechanical checklists, spreads, and footnote conventions. [Paid] [Intermediate]
• Michael Mauboussin & Dan Callahan, "What Does an EV/EBITDA Multiple Mean?" (2018) and "The Math of Value and Growth" (2020): the two best short papers ever written on decompressing multiples; free PDFs. [Free] [Intermediate]
• Mauboussin, The Base Rate Book (2016): growth-persistence base rates for the premium-multiple checklist. [Free] [Intermediate]

Live data. Standing sources; bookmark all of them.

• Damodaran Online (NYU Stern): current-year datasets covering PE Ratio by Sector, Price and Value to Book Ratio by Sector, EV/EBITDA and EV/Sales by Sector (US, Europe, emerging incl. India), plus his January "Data Update" posts walking through each; use these as your sector-level sanity anchors. [Free]
• screener.in (India: financials, peer tables, shareholding/pledge data); stockanalysis.com and TIKR free tier (US: financials + consensus forwards); Trendlyne (India consensus estimates). [Free/Freemium]
• SEC EDGAR: 10-K notes for leases/SBC; DEFM14A merger proxies for fairness-opinion comps and precedent tables. BSE/NSE announcements and SEBI letters of offer (sebi.gov.in) for Indian deal terms and open-offer pricing. [Free]

Video & courses.

• Damodaran's NYU Valuation course (free, YouTube + his site): the relative-valuation / pricing sessions (typically sessions 14–17 of the spring class), with slides. [Free] [Intermediate]
• Zerodha Varsity: Fundamental Analysis module's valuation chapters for India-flavored reinforcement of P/E, P/B, EV basics. [Free] [Beginner]
• CFA Level II equity readings on market-based valuation (price and enterprise multiples), a clean drill bank if you have curriculum access. [Paid] [Intermediate]

India context.

• Saurabh Mukherjea, The Unusual Billionaires and Coffee Can Investing: the quality-scarcity thesis from its strongest advocates; read alongside the growth-duration math above and form your own view of where argument ends and flow-driven pricing begins. [Paid] [Beginner]
• Marcellus and Ambit "quality premium" notes vs. critiques of the same (search "expensive quality India debate"). Read one of each, deliberately. [Free] [Intermediate]

Advanced/reference.

• Pablo Fernandez, "Valuation Using Multiples: How Do Analysts Reach Their Conclusions?" (SSRN): evidence on how sloppily multiples get used in practice; an inoculation. [Free] [Advanced]
• Damodaran's blog posts on pricing vs value ("Musings on Markets"; search "pricing" and the annual multiple posts). [Free] [Intermediate]

Going deeper.

• Michael Mauboussin & Dan Callahan, "Everything Is a DCF Model" (Morgan Stanley Counterpoint Global, 2021; free PDF, check the current link): the cleanest statement of the thesis here, that every pricing method is a compressed discounted-cash-flow model; read it to cement why the rule is "decompress, don't rank." [Free] [Intermediate]
• Aswath Damodaran, The Dark Side of Valuation (3e): the chapters on pricing loss-makers, young/high-growth firms, and cyclicals extend the depressed-denominator and loss-maker rules from comps cleaning (EV/Sales as the multiple of last resort; normalizing cyclical earnings before any trailing multiple). [Paid] [Advanced]

The Modern Analyst's Addendum

Everything above teaches this skill from first principles, by hand. That's how you learn it, and the mastery check still tests it that way. This addendum shows how a working analyst amplifies the same skill today. It adds; it never replaces. (R1/R10)

AI-Augment this skill

{
  "skill": "Decompressing every standard multiple into its drivers, enforcing the claim-level grammar, choosing and cleaning a comp set, aggregating it, fitting the sector line, reading precedent transactions and control premia, and running India's premium-multiple growth-duration discipline",
  "use": "Relative valuation is the module where a tool is most useful on the *inputs* and most dangerous on the *verdict*, because the verdict is a median and a median is exactly the kind of confident number a language model will manufacture. Four uses that survive scrutiny. (1) ADVERSARIAL PEER SEARCH, which is the highest-value use and the one nobody runs: give it your set and ask it to name every listed company you excluded that a reasonable analyst could have included, and to argue each one in on business-model grounds. The Quant lens below shows the peer set moves the answer by more than the analysis does, so the honest defence of a comp set is a documented list of the names you rejected and why — a tool that has read every peer tab is a good generator of that list. (2) NORMALIZATION EXTRACTION: point it at a filing and have it locate the lease-liability note, the share-based-compensation line, capitalized development spend, the associate's carrying and market value, minority interest and the diluted share reconciliation — the tedious inputs to the section 4.7 step-3 EV build, where errors are clerical rather than conceptual. (3) FAIRNESS-OPINION MINING: a DEFM14A reproduces the bankers' entire comps and precedent tables; ask it to pull those into a structured table with the date, consideration mix and unaffected-price basis of each deal, which is the screening data section 4.8 demands. (4) STORY TRANSLATION: hand it the (g, N, ROE) triple your two-stage inversion produced and ask for the operating world in which that triple holds — units, share, distribution, category size — so the multiple becomes falsifiable.",
  "tools": ["Chat assistants — Claude, ChatGPT for adversarial peer nomination, for arguing each admit and reject, and for translating an implied (g, N, ROE) into countable operating units", "Document/PDF AI — for lease, SBC, capitalized-development, associate and minority-interest notes across filings, and for pulling the comps and precedent tables out of a DEFM14A fairness opinion", "Coding assistants — for the EV build as a function with one enforced lease convention, the aggregation with its dispersion, the peer-set sensitivity sweep and the multiple inversions below"],
  "prompt": "Here is my comparable set for <COMPANY>: <NAMES, with the one-line business-model reason each is in>. Task 1: name every listed company I have excluded that a reasonable analyst could defend including, and for each give the strongest one-sentence argument FOR inclusion and the strongest against — I want the set I did not build, not agreement with the set I did. Task 2: for each of <NAMES>, tell me from the filings where to find the lease liability, the SBC expense, any capitalized development spend, the market value of listed non-operating stakes, and the minority interest, citing note numbers. Do not compute any multiple, do not tell me which name is cheap, and do not give me a peer median — I am doing the arithmetic.",
  "verify": "Two verifications, and the second is the one that decides whether the table is analysis or decoration. First, the grammar and the cleaning: run the claim-level check on every column yourself (equity numerator with equity denominator, enterprise with pre-interest), then confirm one lease convention applies to every row, SBC is expensed everywhere, and the time basis is trailing-with-trailing or forward-with-forward. A tool will produce an EV/EPS column without blinking, and section 4.2 says that column fails the module. Second, the peer set: re-run your aggregate on every plausible subset of the names, not just the one you chose. If the verdict flips sign when a defensible name enters or leaves — and the Quant lens shows that it does — then your finding is a peer-selection artifact and must be reported as a range with the set stated, not as a number. Never accept a base rate, a control-premium statistic or a sector multiple from a chat window: pull Damodaran's current-year sector tables, the Mergerstat premium series or the letters of offer yourself, because the one thing a fluent model reliably produces is a plausible-sounding frequency with no source (Guardrail 1-5).",
  "diy": "The gate is unaided: you derive justified P/E, P/B, EV/EBITDA, EV/Sales and EV/IC from the Gordon model on paper, build an enterprise value line by line including the treasury-stock-method dilution, fix a cross-border lease and SBC table by hand, compute a median and a harmonic mean, fit a two-variable OLS line with a calculator, and invert a premium multiple to the growth and duration it requires. Nothing in this callout is admissible in that room."
}

Modern Data Analysis

By hand first. You derived every justified multiple from P0 = D1/(r−g), and built Cascade's enterprise value line by line to $12,666m through the treasury-stock method. You unwound the Bluegrass–Kaveri lease and SBC table until an apparent 16% discount became a 2.5% gap. You fitted the six-bank P/B-on-ROE line by hand, and inverted a 45× trailing multiple into the twenty-five years of 14% growth it demands. Keep all of it. A comps table is arithmetic a schoolchild could do, so code doesn't add arithmetic. It adds something else. The two things that actually decide the answer, the cleaning convention and the peer set, stop being matters of willpower and become properties of the program.

Today's workflow. Write the table as three functions instead of a spreadsheet.

• enterprise_value(row, lease="inclusive"): the step-3 EV build from the ten-step comps build, as code, with the lease convention as an argument. One call site sets it for the whole table, so the Kaveri error becomes impossible to write, which beats being warned about it. Switching the convention re-prices every row at once, so you can watch the switch move the ranking.
• aggregate(multiples) returns the median and the harmonic mean and the set's own dispersion, because a median printed without the spread of the numbers it summarizes is the most-quoted number in valuation, and the least informative.
• verdict(target, peers) takes the peer set as an explicit argument, so you can sweep it. No spreadsheet has this function, and it's the one that keeps you straight.

Written that way, three things become available. First, the aggregate arrives with an error bar. You report 19.9× (peers span 14.9–28.7×) instead of 19.9×. Second, the peer-set sensitivity becomes exhaustive. You enumerate every subset, and not just the two you happened to try. And third, the inversions become root-finds. scipy.optimize.brentq on the trailing-P/E identity returns Saraswati's implied 9.26% in microseconds, and on the two-stage engine it returns the 15.79% that P15's 48× requires. Decompressing a multiple then costs nothing, so you do it for every row, and not only for the one name you already had a view on.

Tools & sources (IN + US). pandas for the table and the filing joins, numpy for the aggregation and the OLS fit, scipy.optimize.brentq for every multiple inversion, itertools.combinations for the peer-set sweep, matplotlib for the value-creation plot with its fitted line. India: the consolidated annual report for the Ind AS 116 lease-liability note, Ind AS 38 capitalized development spend, associate carrying values and minority interest, screener.in peer tabs and exports for the driver columns (ROCE, growth, net debt/EBITDA) and for shareholding and pledge data, NSE and BSE company pages and announcements for the price and share count, Trendlyne for consensus forward estimates where coverage exists, SEBI letters of offer at sebi.gov.in for open-offer price build-ups under the 2011 Takeover Regulations, and AMFI's monthly data at amfiindia.com for the SIP run-rate that the flow argument for India's premium rests on. US: EDGAR's XBRL companyfacts endpoint for machine-readable histories (OperatingIncomeLoss, Revenues, ShareBasedCompensation, MinorityInterest and the operating-lease liability tags) so the driver columns are pulled instead of typed, DEFM14A merger proxies for the bankers' own comps and precedent tables, Damodaran's current-data page at pages.stern.nyu.edu for the PE Ratio by Sector, Price and Value to Book Ratio by Sector and EV/EBITDA and EV/Sales by Sector tables as the absolute-level sanity anchor a comp set cannot provide, FRED's DGS10 for the rate regime that enters every denominator of (r − g), and stockanalysis.com for US consensus forwards.

# What a comp median explains — run on the module's own §4.7 IT table. R3, recomputed in-session.
import numpy as np, itertools
mcap  = np.array([1250000, 650000, 470000, 260000, 155000, 155000.])   # ₹ crore, §4.7 Build 1
ncash = np.array([  48000,  35000,  25000,  35000,   7000,   9000.])
ebit  = np.array([  62500,  34300,  21600,  15100,   5150,   5500.])
m   = (mcap - ncash) / ebit          # 19.23 17.93 20.60 14.90 28.74 26.55  — matches §4.7
med = np.median(m)                   # 19.92× — the table's own headline
r2  = lambda y, p: 1 - ((y - p) ** 2).sum() / ((y - y.mean()) ** 2).sum()
print(f"{med:.2f}x  R2={r2(m, med):+.3f}  mean|dev|={abs(m - med).mean() / med:.1%}")
#   -> 19.92x  R2=-0.085  mean|dev|=19.9%      the median explains none of the dispersion
for i, nm in enumerate(["TCS", "Infosys", "HCLTech", "Wipro", "TechM", "LTIM"]):
    s = [np.median(m[list(c)])                       # every 3-name set from the other five
         for c in itertools.combinations([j for j in range(6) if j != i], 3)]
    print(f"{nm:8s}{m[i]:6.2f}x -> {m[i]/max(s)-1:+6.1%} .. {m[i]/min(s)-1:+6.1%}")
#   HCLTech  20.60x -> -22.4% .. +14.9%          the peer set chooses the sign

Verify. Before the engine touches a live table, prove it against the worked figures above. Start with Deccan's one value in four shirts: EV ₹6,125 crore, with EV/EBITDA 5.83×, EV/EBIT 8.33×, EV/Sales 1.46× and EV/IC 1.67×, each matching its driver formula to four decimals. Then Cascade's build: 4.50m net new shares, 204.5m diluted, EV $12,666m, 6.43× pre-rent and 6.85× on the mismatched denominator. The cross-border pair should resolve to 8.00× and 7.80×, and the four-peer harmonic mean to 17.14× against an arithmetic 26.25×. The six-bank fit should give a slope of 0.2693, an intercept of −1.6744 and R² of 0.9674, with a 14%-ROE bank predicted at 2.096×. Saraswati's 30× should invert to 9.2637%. The two-stage engine should return 65.79× for 16% over 25 years and 45.39× for WE6 Case A, and P15's 48× should solve to 15.7913%. There's one convention to hold straight when you code the return budget. Multiple drag compounds, so the exact expression is (1+g)×(exit/entry)^(1/N) − 1, while the familiar shorthand subtracts the annualized drag from growth. At 13% growth and a fall from 65× to 45× over ten years, the drag factor is −3.6105%/yr. The two forms give 8.9202% and 9.3895%, a 0.47-point gap that widens to 0.97 points on a derate from 65× to 30×, because the linearization drops the cross-term. Both are recognizable. A code implementation must say which it used, and the compounding form is the one that reconciles with a price series. On the cash multiples, an enterprise value of ₹5,000 crore over cash from operations of ₹500 crore reads 10.0× naively and 8.93× once ₹60 crore of after-tax interest is added back, so the naive form overstates by 12.0%. Cash earnings of ₹4.90 a share at ₹42 give 8.57×, against a 14.0× price to earnings and a 16.15× price to free cash flow to equity. A ₹0.70 earnings surprise on a ₹0.28 surprise standard deviation is a standardised unexpected earnings of +2.5. That's a momentum reading, and it isn't a valuation.

Quantitative lens

The two comp tables above are enough to measure something the practice never quotes. How much of a peer group's dispersion does the median actually explain, and how much of the answer did the analyst choose when they chose the set? All figures below come from the code above and its extensions. They were run in-session on the two comps tables and on a controlled panel generated from the EV/EBIT driver formula derived earlier. They're properties of those inputs, and they measure no company.

The comp median is a model with an R² of zero and no error bar. Take the six Indian IT names at their EV/EBIT multiples of 19.23×, 17.93×, 20.60×, 14.90×, 28.74× and 26.55×. The median is 19.92×, the table's own headline. As a predictor of a peer's multiple it scores R² = −0.085, which is worse than predicting the mean, and the mean by definition explains nothing. That's no criticism of the median. It's simply what a constant is. The consequence is the part that matters. The average peer is 19.9% away from that median, and the root-mean-square distance is 25.3%. So the sentence "it trades at a 20% discount to the peer median" describes a company standing at the average distance a peer stands from the median. On the US beverages table the arithmetic is worse: median 20.97× EV/EBITDA, mean absolute deviation 27.5%, R² −0.002. A discount has to clear the set's own dispersion before it's even a candidate for a finding, and almost no published comp note reports that dispersion.

Change the peer set and you change the answer, by more than the analysis changes it. Judge each IT name against every three-name set you can draw from the other five. There are ten of them, and all are defensible on a business-model argument. HCLTech at 20.60× reads anywhere from 22.4% below peers to 14.9% above. That's a 37-point band containing both verdicts, and the analyst picks. Tech Mahindra reads +39.5% to +60.3% and Wipro −43.9% to −22.5%. Those two keep their sign, so the direction survives. The magnitude doesn't, and the magnitude is what gets into the price target. The band narrows as the set widens. Taking five of the six names moves the median across only 6.9%, four of six across 25.1%, and three of six across 43.3%. So the instruction to aim for five to eight names and document every admission is more than tidiness. It's the only control on the largest single degree of freedom in the method, and that makes publishing the rejects the habit that counts. The US set behaves the same way. Three of the five beverage names put the median anywhere from 14.69× to 24.76×, a 48% span.

A six-name table can't tell you how much the drivers explain, or what the standard shortcut throws away. With six points and three regressors you have two residual degrees of freedom and an R² that means nothing. Fitting ROCE alone to the IT set gives R² 0.063 and an adjusted R² of −0.171. So generate a panel from the same algebra instead. Take 590 firms with EV/EBIT = (1−t)(1−g/ROIC)/(WACC−g), growth uniform on 1 to 8%, ROIC on 8 to 40%, WACC on 9 to 14% and tax at 25%, all multiplied by lognormal pricing noise of 20%. Knowing every firm's true driver value scores R² = 0.805. That's the ceiling, and the missing 19.5% is the noise, by construction. Against that ceiling, the comp median scores −0.055. A linear fit on ROIC alone scores 0.111, on growth alone 0.160, on WACC alone 0.276, and on all three together 0.568. Add the two terms the theory actually specifies, g/ROIC and 1/(WACC−g), and the fit reaches 0.774, essentially the ceiling. You can read that two ways, and both are useful. The drivers do own the multiple, which is the central claim of the driver algebra, now measured. And the linear version of that intuition ("adjust the peer multiple for growth and returns") captures about 73% of what the algebra captures. The algebra is convex in growth and hyperbolic in WACC − g, while the mental adjustment is a straight line. Regressing multiples on fundamentals is a large improvement on a median, and it's still a lossy approximation of a formula you already know.

Inside a tight peer set, the median is right about direction and useless about size. Repeat the panel with the drivers deliberately squeezed to what a well-pruned set looks like: growth 4% ± 1 point, ROIC 18% ± 4 points, WACC 11% ± 0.8 points, same 20% pricing noise. Even there the drivers explain only 43.4% of the observed dispersion. The rest is pricing noise, and that's the plain reason a clean comp set still produces a wide table. Judge a firm against an eight-name median drawn from that same tight sector, and the verdict runs from −30.2% at the 10th percentile to +44.4% at the 90th. It agrees with the firm's true cheap-or-dear status 76.5% of the time. That's the fair defence of the practice, stated as a number. Three times in four the median gets the sign right, so a comps table is worth the minutes it takes to build. It's also the limit. The same exercise says nothing usable about how much, and selecting five of ten available peers moves the median by a median of 39%. That's more than the typical real mispricing anyone is hunting.

A comps table also can't see the level of the room. Price each of the six IT names off the single-stage enterprise algebra at the India anchors (WACC 11.5%, tax 25%), using each firm's stated growth and ROCE. Justified EV/EBIT runs 6.52× to 9.62×, against market multiples of 14.90× to 28.74×. Every name in the table trades between 1.89× and 4.20× its single-stage justified multiple, with a median of 2.22×. Read that correctly. It doesn't say Indian IT is 2.2× overvalued. A single-stage model at 4% perpetual growth is a deliberately austere benchmark. The whole argument about India's premium multiples is that a premium multiple is a claim about duration, which single-stage arithmetic can't represent. What the ratio measures is the size of the growth-phase claim the whole sector is carrying. 55% of each price lies outside anything a steady state can justify, and a comps table that ranks these six against each other can't see one rupee of it. That's the 1999 Cisco warning from the start of the core content, quantified on these same numbers. It's also the reason the phase capstone puts a DCF and a reverse DCF on the same page as the comps.

Now the limits, stated plainly, because a table of six numbers is the easiest place in valuation to over-conclude. The two comps tables are labelled illustrative and modelled on FY25/CY24 scale. Each figure above is a property of those numbers, and rebuilding them from live filings will move each one. The method transfers, and the decimals don't. The panel results are shakier still. The driver distributions and the 20% pricing noise are assumed, and the R² values move directly with them. Widen the ROIC range and ROIC's share rises. Cut the noise and every R² rises toward one. So re-run the decomposition with your own sector's dispersion instead of quoting 0.774. The panel also holds the functional form true by construction, and that's the strongest assumption here. Real multiples are set by a market that isn't obliged to price any formula, and the ceiling of 0.805 exists only because I generated the truth. The peer-set sweep enumerates subsets of a set someone already chose. So it measures the manipulability within a candidate list and understates the full degree of freedom, which begins at "who is a comparable at all." And the 76.5% direction-agreement figure is agreement with a model's fair value, and says nothing about a realized return. Nothing above is evidence that trading on peer-relative cheapness makes money, and the data here can't answer that question. What the numbers do support is narrow and worth having. Report the median with the set's dispersion, publish the peer set and its rejects, and treat any gap smaller than the set's own spread as noise.

Do it in code: build EV as a function with the lease convention as an argument. Return the median with the harmonic mean and the dispersion. Sweep the peer set exhaustively before you write a sentence about a discount. Fit the sector line and read the residual as a question. Invert every premium multiple with a root-find instead of eyeballing it. Then anchor the whole table against one absolute check that the comp set can't supply. See G1/QM1.02, G2/DA1.02 and G2/QD1.02.

Where this goes next: galaxy cross-links

• G1 · QM1.02 Hypothesis Testing & Regression: R², adjusted R², residual standard error and degrees of freedom, and what the six-point bank fit can and cannot support, and how to report a sector line with the uncertainty that makes a residual a testable claim rather than a hunch.
• G1 · QM1.01 Probability, Distributions & Estimation: the sampling distribution of a median, why a six-name aggregate has an error bar at all, and the difference between a spread across peers and a confidence interval on the number you quote.
• G2 · DA1.02 Pandas Data Wrangling: the comp table as a dataframe with a schema. One lease convention applied to every row by construction, filing joins that survive a restatement, and an EV build you can re-run when a price moves.
• G2 · QD1.02 Signal & Factor Construction: neutralising a multiple against its drivers is factor construction. The residual the bank regression calls a question is a cross-sectional signal, and the work here shows how it is built, standardized and tested rather than eyeballed.
• G2 · DA1.04 EDA & Visualization: the value-creation plot done properly: EV/IC against ROIC with the fitted line, the (WACC, 1.0×) anchor drawn, and every point labelled so the off-line names are visible instead of buried in a column.
• G3 · CN1.02 Hypothesis-Driven Problem Solving: a residual is a hypothesis; this is the habit of stating it, naming the evidence that would settle it, and going to get that evidence before the table becomes an opinion.

Teach it back & journal

Feynman prompt. Explain to a smart 15-year-old why two dosa stalls, each selling the same ₹1,000 of dosas a day, can fairly deserve different price tags as businesses. Walk her through it stall by stall. One owns an expensive griddle that wears out (your d). One keeps more of each rupee (your margin and tax). One must spend most of its profits on a second griddle to grow (your g/ROIC). And the last is on a street where stalls rarely stay busy for long (your r and duration). Then write the one-page explainer: "A multiple is a price with its story amputated: here is how to sew the story back on." You have to get through the whole page without the words "justified," "WACC," or "terminal." If a step needs jargon to survive, you haven't understood that step yet.

Journal reflection. Find the last time you called something "cheap" or "expensive" off a single multiple column. It counts if it was a note you read or a screen you ran. There's almost certainly one in your recent past. Rerun it properly tonight. Attach the driver columns, normalize the one accounting difference that matters most, and locate the residual. Write down whether the verdict survived. Then answer the harder question in writing: when I see a 65× P/E on a beloved Indian compounder, is my first reaction to sneer or to surrender? Whichever it is, that's your bias. Record the step from the premium-multiple checklist you'll force yourself through, every time, before that reaction gets to vote.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.