The Map, the Machine & the Five Questions

Phase 0 · Orientation & Foundations · Week 1 · ~8 hours of module work

Somebody paid ₹4,000 this morning for a claim called "DMART." Not for a shop, not for a shelf of atta and soap you could stand in front of and touch. For a claim.

You probably can't say yet why that was a sane thing to do, and nothing here assumes you know anything else about finance either, starting with what a balance sheet is. The Master Map in your Library is the blueprint of the whole path. Keep it open while you work, and come back to it whenever you want to see where a module fits. The numeracy bootcamp runs alongside in the same week, and how capital markets work follows in week 2.

By the end you'll carry the two ideas that organize the entire program. The first is the five questions every business analysis answers. The second is the master idea: a business creates value only when it earns more on the money inside it than that money costs. You'll also have taken a placement diagnostic, so the program starts where you are.

Units, used throughout: ₹1 lakh = 100,000; ₹1 crore = 10 million (100 lakh); US figures in $m and $bn. ₹1 crore ≈ $115–120k at recent exchange rates (as of mid-2026).

Your ~8 hours: core content with notes (3.0h) · worked examples + practice set (2.0h) · diagnostic, scoring, placement decision (1.0h) · mini-project (1.5h) · mastery check, teach-back, journal (0.5h).

Learning objectives

You will be able to:

1. Explain from first principles why businesses exist (surplus, specialization, exchange) and why capital markets exist (matching savings to enterprise; making ownership claims liquid), with numbers.
2. Define a share precisely, as a proportional claim on a business's future cash flows, and use it to distinguish investing from speculation.
3. State the five questions from memory, in order, explain what each asks, and why price comes last.
4. State the master idea, that value is created only when ROIC exceeds the cost of capital and the business can reinvest at that spread, and demonstrate it with a numeric example in which the faster-growing company is worth less.
5. Trace how ₹1 of DMart's sales and $1 of Costco's sales becomes profit, and explain why both choose thin margins deliberately.
6. Compute a simple ROIC (profit ÷ capital tied up), an economic profit ((return − hurdle) × capital), and an implied yield (annual owner cash ÷ price).
7. Navigate the program: the eleven phases, the signature skill, the mastery-gate rules, the weekly template.
8. Take the 20-question placement diagnostic, score it, and make a rule-based placement decision.

Prerequisites & connections

Builds on. Nothing. You need school arithmetic: percentages, multiplication, reading a table. If those feel shaky, the numeracy bootcamp that runs in parallel this week repairs them. Start it alongside, not instead.

Builds into. Everything. How capital markets work opens the machine room behind the "why markets exist" story told here: exchanges, order books, settlement, SEBI/SEC/RBI. The numeracy bootcamp formalizes the compounding arithmetic used casually here. The toolkit installs the knowledge system, and the guided annual-report read turns the mini-project's first contact with DMart and Costco into a full read of both reports. Phase 1 teaches the language in which question 1 is answered properly. Phase 2 teaches when to distrust it. Phase 3 turns the "hurdle rate" hand-wave below into a formal cost of capital, and nothing here needs the WACC machinery that arrives with it. Phases 4 and 5 answer question 2 in depth. Phases 6 and 9 build temperament, Phase 7 supplies the macro weather, and Phase 8 compresses everything into the signature teardown and deep dive, certified in week 69. The five questions you memorize this week are the spine of the weekly company reads that begin in week 5.

Core teaching content

4.1 Why businesses exist: surplus, specialization, exchange

Strip everything away and start with two people.

Asha farms. In a good season she grows more grain than her family eats, and that extra is a surplus. Bharat cobbles. He can make four pairs of sandals in the time it would take him to grow one sack of grain, badly. Left to themselves, each does everything poorly.

The moment they specialize, total output rises, because each hour goes where it produces the most. Problem 1 has you compute the gain, so you don't have to take it on trust. Specialization then creates a new problem, because each of them now holds what the other needs. Money solves it. Everyone accepts the token, so anyone can sell to whoever wants their output and buy from whoever has what they need. A market is any arrangement where buyers and sellers meet and prices form, and it coordinates thousands of strangers with nobody in charge.

A business is this value creation organized to repeat at scale. It buys inputs, from materials and labor to equipment and money itself. It transforms them and sells output that customers value more than the inputs cost. That gap is where profit comes from.

If you keep one sentence from this section, keep this one. Profit that's earned fairly and reported straight is the measurement of value created for others. A grocery chain that buys toothpaste at ₹80, moves it near your house, and sells it at ₹95 created ₹15 of place-and-time convenience you willingly paid for. If that survives rent, salaries, and electricity, the leftover profit certifies the whole chain of activity was worth doing.

Two caveats, so you never hold this naively. Reported profit is a human-made number and can be manipulated, and Phase 2 exists to catch that. Profit can also coexist with harm the price doesn't capture: pollution, deception, monopoly abuse. The ethics-and-governance thread exists for those. The first principle still stands. Specialization plus exchange creates value, and a business is a repeatable machine for doing it.

4.3 Why ownership claims trade: liquidity, price, and Mr. Market

Suppose shares could never be resold, so whoever bought at the founding held until the company died. Would you buy? Only at a huge discount, because your money would be hostage for decades.

Flip that around and you have the deep reason secondary markets exist. In a secondary trade, investors sell existing shares to each other, and the company receives nothing.

Liquidity, the ability to exit at a fair price at any time, makes strangers willing to commit capital in the first place, and to accept a lower return for it. Because you can sell any minute, you'll fund a factory that takes twenty years to pay off. Liquid markets make patient capital cheap, and that's the social function of the flickering screens. The machinery behind it gets its own week: exchanges, order books, brokers, depositories, settlement, indices, SEBI/SEC/RBI.

But liquidity has a psychological price. Once your claim is repriced every second, it is easy to forget it is a claim on a business at all.

Fix the distinction now, permanently. Price is what the market will pay today, the outcome of the most recent trades between whoever showed up. Value is what the claim is worth, meaning the cash the underlying business will generate over its remaining life, and nothing else. Benjamin Graham's metaphor compresses it. You own a shop with a partner, Mr. Market, who every day names a price at which he'll buy your half or sell you his. Euphoric some days, despondent others, never offended when ignored, always back tomorrow.

Most of the work of investing is refusing to let his mood become your estimate of value. Price is an offer, not a verdict.

One reframe to keep forever. When DMart's price moves 3% in a day, the stores and trucks and people haven't changed. What moved is the market's aggregate expectation of the future. Prices are expectations made visible, and question 5 treats them that way.

4.7 One rupee into DMart, one dollar into Costco

Follow the money at intuition level for now. Phase 1 will let you rebuild these walks from the filings yourself. All numbers are illustrative, modeled on ~FY24/FY25 scale, so pull the actual filing. DMart's annual report is on its investor-relations page or NSE/BSE, and Costco's 10-K is on SEC EDGAR.

DMart: ₹100 walks into a store. Avenue Supermarts, on roughly FY25 scale, has revenue of the order of ₹59,000 crore and net profit around ₹2,700 crore. Per ₹100 of sales:

₹4.75 kept per ₹100 looks feeble until you remember margin × turnover. DMart sells through its inventory roughly every 3 to 4 weeks, which is 11 to 14 stock turns a year. Each rupee of capital generates several rupees of annual sales, and its return on capital employed comes to around 20% (illustrative) against an Indian hurdle of ~12%. That's a wide, persistent spread.

So the thin margin is strategy. Pricing below everyone else packs the stores and spins the inventory, and the volume that comes back through the door is what makes the low prices affordable to offer in the first place. A fat-margin DMart would be a slow, beatable DMart. As a preview, the moat is a cost advantage that DMart spends on lower prices instead of keeping as reported margin. And DMart reinvests essentially all profit into new stores. That's reinvestment at a high spread, the compounding engine from the lemonade ledger.

Costco: $1 walks into a warehouse. On roughly FY24 scale, total revenue is about $254bn, made of merchandise sales ≈ $250bn plus membership fees ≈ $4.8bn, and net income is about $7.4bn. Of each $100 of merchandise sales, about $89 goes to suppliers, a gross margin of ~11% that's roughly two-fifths of a typical supermarket's. About $9 covers warehouses and wages. That leaves $2-and-change from actually selling things.

So where's the money? The astonishing line is elsewhere. Membership fees arrive with almost no incremental cost and amount to roughly half of the ~$9.3bn operating income, and worked example 4 does the arithmetic. Costco turns inventory ~12 times a year and collects immediately while paying suppliers on ~30-day terms, so suppliers largely finance the inventory on the floor. Renewal rates run ~90% (illustrative, so check the 10-K), and the fee stream behaves almost like subscription revenue.

Read the two models side by side:

The countries differ, and so do the currencies and mechanisms. The deep structure is identical: modest margins, ferocious capital productivity, a durable spread over the hurdle and decades of reinvestment. Every Phase 5 sector playbook is a variation on reading a table like this.

4.8 The map of the program: 80 weeks, eleven phases, one skill

All of it leads to a signature capability. You'll be able to form a structured understanding of any business in 1–2 hours, and know essentially everything that matters after a 2–3 day deep dive. That gets certified in week 69 on companies you've never seen, then proven twice at institutional grade in Phase 10. Everything between is sequenced to make it possible:

The five questions organize even the calendar. Phases 1 and 2 make you fluent in Q1's raw material and guard against being lied to. Phases 3 to 5 quantify Q2 and Q5 and deepen Q1. Q3 and Q4 accumulate everywhere, with dedicated machinery in 3.07, 6, 7 and 9. Phase 8 compresses all five into two repeatable formats.

The weekly operating system takes ~25 hours, and the hours are fixed. Module work takes ~16h. The ~3h daily loop is 30 min × 6 days of due flashcards, then app drills. The company of the week takes ~2h: from week 5, one real company every Saturday, India and US alternating, with the standard rising, for ~60 companies before Phase 8. The ~3h reading spine is Zerodha Varsity and Piper in this phase, and ~1h goes to the Sunday review and journal. If a week gets crowded, protect the daily loop above everything. It's the difference between "studied once" and "knows."

The rules that make it real are the nine working agreements from the master map, digested. Mastery gates are sacred at ≥85%, and crown gates at ≥90%. If you miss, you retake a different form after two-plus days. Write your answer fully before looking at any solution. Every concept touches a real company within 48 hours. India and US, always both. The journal is written before outcomes and never edited after. Primary sources outrank every summary. Process counts for more than outcome. And none of this is investment advice. DMart and Costco included, every company here is a teaching specimen and never a recommendation.

4.9 The self-placement diagnostic

Twenty questions, four sections. Take it closed-book, alone, in 45–60 minutes, before reading the answer key. Its purpose is placement, and nobody is judging you. There's no pass or fail, and if you're a true near-beginner you should expect a low score, since the course is built for you. Mark guesses with a ? and treat lucky ?-hits as wrong when placing yourself. The app's onboarding runs a shorter placement check of its own. It asks up to twelve short questions, six on Phase 1's financial statements, and six more from Phases 2 and 3 only if you get all six right. It can start you anywhere from Phase 0 to Phase 3, and it opens every phase up to that one, though it marks no module passed. Treat this twenty-question version as the fuller self-assessment. Where the two disagree, the rubric below is the stricter test, and the app lets you start from Phase 0 instead.

Section A — Numeracy & money basics

A1. A stock rises 15% in year one and falls 15% in year two. ₹800 invested becomes: (a) ₹800 (b) ₹782 (c) ₹818 (d) ₹770

A2. ₹1,00,000 compounds at 8% per year for 3 years. Final amount (nearest rupee)?

A3. Your fixed deposit pays 7%; inflation is 5%. Your real return, the gain in what you can actually buy, is approximately: (a) 12% (b) 7% (c) 2% (d) 5%

A4. A portfolio is 60% in asset X returning 10% and 40% in asset Y returning 5%. The portfolio return is ___%.

A5. A shirt's price was cut by 20% and now sells for ₹400. The original price was ₹___.

A6. A venture has a 50% chance of paying ₹200 and a 50% chance of losing ₹50. Its expected value is ₹___.

Section B — Accounting & statements

B1. Which statement shows what a company owns and owes at a single point in time? (a) income statement (b) balance sheet (c) cash flow statement (d) annual report cover

B2. Under accrual accounting, revenue is recorded when: (a) cash is received (b) the order is placed (c) the goods/services are delivered (earned) (d) the financial year ends

B3. A company has assets of ₹500 crore and liabilities of ₹300 crore. Shareholders' equity is ₹___ crore.

B4. A firm buys a ₹10 lakh machine that will last 10 years. Good accounting will: (a) expense ₹10 lakh immediately (b) never expense it (c) spread ~₹1 lakh of expense over each of 10 years (d) expense it when the machine is sold

B5. A company sells ₹50 lakh of goods on credit (customer hasn't paid yet). This period, reported profit and cash received change by, respectively: (a) +₹50L and +₹50L (b) +₹50L (less costs) and ₹0 (c) ₹0 and ₹0 (d) ₹0 and +₹50L

B6. In double-entry bookkeeping, to increase an asset account you ___ it: (a) debit (b) credit (c) either (d) close

B7. Which statement reports cash actually received and spent during a period, sorted into operating, investing, and financing? (a) income statement (b) balance sheet (c) cash flow statement (d) statement of changes in equity

Section C — Markets & instruments

C1. The essential difference between a bond and a share: (a) bonds are riskier (b) a bondholder has a fixed claim (interest + principal); a shareholder owns the residual, whatever is left (c) shares pay guaranteed dividends (d) bonds trade only privately

C2. A company sells new shares to the public for the first time (an IPO) in the ___ market; when those shares later change hands between investors on the NSE or Nasdaq, that is the ___ market.

C3. The Nifty 50 and the S&P 500 are: (a) companies (b) regulators (c) indices — measuring sticks tracking a basket of listed companies' prices (d) mutual funds

C4. A company earns ₹20 per share this year and its share trades at ₹500, a P/E of 25. This means: (a) the price will rise 25% (b) you are paying ₹25 for each ₹1 of current annual earnings (c) dividends are ₹25 (d) the company is 25 years old

Section D — Analysis & valuation intuition

D1. Firm X: 12% net profit margin, 8% return on invested capital. Firm Y: 4% net margin, 22% return on invested capital. Both face a 12% hurdle. The better business is: (a) X, for the higher margin (b) Y, for the higher return on capital (c) equal (d) can't say without revenue

D2. A company earns 6% on every rupee it reinvests; its investors' opportunity cost is 12%. If it reinvests more and grows faster, its value per rupee invested: (a) rises (b) falls (c) unchanged (d) depends on the P/E

D3. True or false: a wonderful, honestly run, growing company can still be a poor investment.

Answer key (1 point each; be strict). A1 (b): 800×1.15×0.85 = ₹782. Gains and losses aren't symmetric. A2 ₹1,25,971 (1,00,000 × 1.08³), and accept ₹1,25,900–₹1,26,000. A3 (c): real ≈ nominal − inflation, and the exact figure is 1.07/1.05 − 1 = 1.9%. A4 8% (0.6×10 + 0.4×5). A5 ₹500 (400 ÷ 0.8). The classic trap is 400 × 1.2 = 480. A6 ₹75 (0.5×200 − 0.5×50). B1 (b). B2 (c): accrual records revenue when it's earned, whenever the cash arrives. B3 ₹200 crore (assets − liabilities). B4 (c): that spreading is depreciation. B5 (b): profit is accrual, cash is cash, and the gap becomes a receivable. B6 (a): pure convention, learned cold when double-entry arrives. B7 (c). C1 (b). C2 primary, then secondary. C3 (c). C4 (b). D1 (b): margin isn't return. Y earns 22% against a 12% hurdle, and X earns 8% and destroys value. D2 (b): reinvesting at 6% against a 12% alternative turns each rupee into ~50 paise, and growth amplifies destruction. D3 True, if the price already assumes more than perfection (question 5 is separate).

Placement rubric. Score each section, then apply the rules. The test-out protocol is always the same. Attempt the target module's Mastery Check Form A cold, closed book, under exam conditions. If you pass at its threshold, log the score, still do that module's flashcards, and move on. If you fail, do the module in full. The diagnostic alone never skips anything. Only a passed mastery form does.

Record in your journal: total and section scores, guesses that landed, your placement decision, and one sentence on how it felt not to know things. You'll re-read it in week 80, and it's usually a kinder read than you'd expect.

Common mistakes & how experts think differently

"The stock is the ticker." Beginners experience a stock as a wiggling price, casino chips with company names on them. Experts hold the ownership frame so firmly it changes their language: "I own 0.5% of this business's future cash flows." When price falls with the business unchanged, their first thought is that the same stream got cheaper. A beginner thinks I am losing. Train the reflex. Every time you see a price, append "…for a claim on the cash flows."

"High margin = good business." This is the most common analytical error at this stage, and DMart and Costco are the standing counterexamples. Margin is one lever and turnover the other. The product is what matters, and the hurdle is the judge. A 3%-margin retailer turning capital fast can beat a 15%-margin manufacturer whose cash sleeps in inventory. Don't praise or damn a margin until you know what return on capital it compounds into.

"Growth is good." Say "growth" to a beginner and they hear value. An expert asks, by reflex, at what return on what capital? Reinvesting at 8% against a 12% hurdle turns ₹1.00 into ~₹0.67, and doing more of it faster destroys value faster, even as revenue and reported profit rise. Applaud growth only after you've seen the spread.

"Profitable = value-creating." Accounting profit ignores the cost of the owners' capital. A business can report profit every year and still make its owners poorer than the alternative. Economic profit, (ROIC − hurdle) × capital, is the analyst's ledger. The accountant's "profit" and the economist's differ by the opportunity cost of capital, and by nothing else.

Starting with the price. Beginners look up the price and P/E first, then form a view, and everything they later "discover" bends toward that anchor. Experts work through questions 1 to 4 before 5 on purpose, and sometimes avoid looking at the price at all until the business work is done. Respect the order mechanically until it becomes taste.

"The market is a casino" and "the market can't be beaten", held as slogans. Both extremes excuse you from work. The defensible position is that markets are mostly right most of the time, so question 5 treats the price as a hypothesis deserving respect. They're also occasionally, identifiably wrong about individual businesses, and that's what lets the signature skill exist. Phases 6 and 9 present the efficient-markets evidence fairly. It's strong enough that most people should index, and the course trains you for the "and yet."

Skipping foundations because the destination is exciting. Valuation models are seductive. Debits and credits aren't. But a DCF built on statements you can't read, or can't distrust, is a spreadsheet-shaped hallucination. Trust the sequence: language, lie-detection, then valuation.

Treating the diagnostic as an ego test. Inflating your placement steals from one person, and it's you. Experts are ruthless about knowing what they don't know. Munger held that knowing the edge of your competence beats brilliance. Practice on yourself first.

Worked examples

Worked example 1: Pricing Sharma's pharmacy (capitalizing a stream, forwards and backwards)

Let's price it together. The pharmacy reliably produces ₹1,00,000/year of owner profit after all costs, including a fair salary for Sharma's hours. Assume the stream is flat and dependable. FDs pay 7% (as of mid-2026).

Step 1: the risk-free benchmark. How much would you need in an FD to produce ₹1,00,000/yr? It's 1,00,000 ÷ 0.07 ≈ ₹14.3 lakh. That's what a safe lakh-a-year costs.

Step 2: demand more for risk. The stream can be disrupted, so you require 12.5%. Your maximum price is 1,00,000 ÷ 0.125 = ₹8,00,000.

Step 3: run it backwards on an asking price. Sharma asks ₹16,00,000. The implied yield is 1,00,000 ÷ 16,00,000 = 6.25%, which is less than the FD, for a riskier stream. At that price you're either overpaying or implicitly betting profits will grow. Make that bet consciously or not at all. This is question 5 in embryo. The price implies a future, so name it, then judge it.

Step 4: the growth peek. If profits grew 5%/yr and you still required 12.5%, the Gordon growth model that the valuation phase builds prices the stream at 1,00,000 × 1.05 ÷ (0.125 − 0.05) = ₹14,00,000. Growth nearly doubled the value. Real, durable growth is enormously valuable, and for the same reason prices that assume it need interrogation.

Worked example 2: Two companies, and why the faster grower is worth less

Two synthetic companies both start with ₹1,000 crore of invested capital, and the hurdle is 12%. Steady Ltd earns an 18% ROIC. Busy Ltd earns 8%. Which would you rather own? Hold your answer while you watch what growth does to each.

Step 1: today's economic profit.

• Steady: after-tax operating profit = 18% × 1,000 = ₹180 cr → economic profit = (18% − 12%) × 1,000 = +₹60 cr/yr.
• Busy: profit = 8% × 1,000 = ₹80 cr → economic profit = (8% − 12%) × 1,000 = −₹40 cr/yr. Busy is profitable and value-destroying at the same time.

Step 2: both "grow". Each reinvests ₹500 crore at its existing return.

• Steady: new profit = 18% × 1,500 = ₹270 cr (+50% growth). Economic profit = 6% × 1,500 = +₹90 cr.
• Busy: new profit = 8% × 1,500 = ₹120 cr (also +50% growth). Economic profit = −4% × 1,500 = −₹60 cr. Destruction grew just as fast as profit.

Step 3: what did each ₹500 crore of growth create? Capitalize the added profit at the 12% hurdle:

• Steady added ₹90 cr/yr (18% × 500) → stream worth 90 ÷ 0.12 = ₹750 cr for ₹500 cr invested: +₹250 crore created.
• Busy added ₹40 cr/yr (8% × 500) → stream worth 40 ÷ 0.12 ≈ ₹333 cr for ₹500 cr invested: −₹167 crore destroyed. Every rupee handed to Busy became ~67 paise.

Step 4: the headline trap. Next year's paper runs the headline "Busy Ltd profits surge 50% on aggressive expansion." Revenue's up and profit's up, yet the owners are poorer by ₹167 crore than if the cash had simply been returned. The identical headline for Steady would describe ₹250 crore of real value created. You can't tell them apart without the spread, so question 2 asks about ROIC versus the cost of capital and never about growth alone.

Worked example 3: The grocer and the jeweler (margin × turns)

Two synthetic single-store businesses each have ₹100 of invested capital, and the hurdle is 12%.

• GroceryMart sells ₹400/yr (capital turns = 400/100 = 4×) at a 5% after-tax margin → profit = 5% × 400 = ₹20 → ROIC = 20/100 = 20% = 5% × 4.
• Aurum Jewels sells ₹100/yr (turns = 1×, because gold sits in the case for months) at a 10% margin → profit = ₹10 → ROIC = 10% = 10% × 1.

Now hold both against the hurdle. GroceryMart's economic profit = (20% − 12%) × 100 = +₹8/yr, and Aurum's = (10% − 12%) × 100 = −₹2/yr. The "premium" business with double the margin destroys value, and the "cheap" one compounds. Every sector in Phase 5 starts with the same question. Which lever does this model run on: margin, turns, or both?

Worked example 4: Costco: finding the real profit engine (question 1 with numbers)

Illustrative FY24-scale figures, to be checked against the actual 10-K in the mini-project:

• Total revenue ≈ $254bn: merchandise sales ≈ $250bn plus membership fees ≈ $4.8bn.
• Merchandise costs ≈ $222bn → merchandise gross profit ≈ 250 − 222 = $28bn → gross margin ≈ 28 ÷ 250 ≈ 11%.
• Operating costs (SG&A etc.) ≈ $23.5bn → profit from actually retailing ≈ 28 − 23.5 = $4.5bn, which is about 1.8% of merchandise sales.
• Operating income ≈ 4.5 + 4.8 = $9.3bn → membership fees ≈ 4.8 ÷ 9.3 ≈ 52% of operating income, from ~1.9% of revenue, at almost no incremental cost.

Interpretation, in five-questions language. On Q1, Costco is paid for access to groceries at cost, a subscription business in a warehouse costume. On Q2, capital recycles fast. With ≈12 inventory turns and ~30-day supplier terms, goods are often sold before they're paid for, and it earns well above the US hurdle. On Q4, what could kill it is whatever threatens the membership's perceived value, which is a wider threat than retail competition. On Q5, a ~50× P/E implies the market expects this engine to compound for a very long time. Reclassify one $4.8bn line and the whole company reads differently. "How does it make money" is a question you answer with numbers.

Worked example 5: What a rupee of retained earnings becomes (India)

Nirmal Foods (synthetic) keeps ₹100 of profit per share instead of paying it out, and reinvests it inside the business. The hurdle rate is 12%. What did shareholders receive for the forgone dividend? Capitalize the new annual profit the ₹100 throws off at the hurdle, using value ≈ cash flow ÷ required return, the tool from the pharmacy.

Step 1: reinvest at a high return (ROIC 20%). The ₹100 now earns ₹20/yr. Capitalized, that's 20 ÷ 0.12 ≈ ₹166.7. Shareholders gave up a ₹100 dividend and received ₹166.7 of value, so ₹66.7 is created per ₹100 retained.

Step 2: reinvest at a poor return (ROIC 9%). The ₹100 earns ₹9/yr, worth 9 ÷ 0.12 = ₹75. They gave up ₹100 of cash for ₹75 of value, so ₹25 is destroyed per ₹100 retained. The dividend they never received was worth more than what management did with it.

Step 3: reinvest exactly at the hurdle (ROIC 12%). ₹12/yr is worth 12 ÷ 0.12 = ₹100. The retention is value-neutral. A rupee kept became a rupee of value, no more.

The point. "The company retained most of its earnings to fund growth" is neither good nor bad news until you know the reinvestment ROIC versus the hurdle. Retention is a silent capital-allocation decision management makes on your behalf every year, and here question 3 meets question 2. A high-ROIC compounder that retains is a gift. A low-ROIC business that retains is a slow leak dressed as ambition.

Worked example 6: What leverage does to owner returns, and to risk (US)

Cascade Tools Inc. (synthetic) has $500m of invested capital earning $60m of after-tax operating profit (NOPAT), an ROIC of 60 ÷ 500 = 12%. Corporate tax is 25%, so pre-tax operating profit = 60 ÷ 0.75 = $80m. Compare two ways to finance the identical machine.

Step 1: all equity. Equity = $500m, no interest, net income = NOPAT = $60m → ROE = 60 ÷ 500 = 12%. With no debt, ROE equals ROIC.

Step 2: add $200m of debt at 6% (equity $300m). Interest = 200 × 6% = $12m. Pre-tax profit = 80 − 12 = $68m, tax at 25% = $17m, and net income = $51m, so ROE = 51 ÷ 300 = 17%. Leverage lifted owner returns by five points. The borrowed $200m works at the business's 12% operating return while costing 6% pre-tax, and that spread accrues to a thinner equity base. So far it looks like free money.

Step 3: the same leverage in a downturn. Operating profit isn't fixed. Suppose pre-tax operating profit falls to $40m in a bad year. All-equity net income = 40 × 0.75 = $30m, so ROE = 30 ÷ 500 = 6%. Levered, it's (40 − 12) × 0.75 = $21m, so ROE = 21 ÷ 300 = 7%. The five-point advantage has shrunk to one.

Step 4: the fixed claim bites. If operating profit falls to $10m, the all-equity firm still earns 10 × 0.75 = $7.5m (ROE +1.5%) and can't be forced under. The levered firm owes $12m of interest it didn't earn. That's a pre-tax loss of 10 − 12 = −$2m, cash it must find from reserves or refinancing. Leverage amplifies the good years, amplifies the bad years worse, and can convert a survivable slump into a solvency problem. For that reason equity, the residual claim with no floor that's paid last, demands a higher return than debt, the fixed claim paid first. These numbers are the skeleton behind the debt-versus-equity distinction drawn earlier. Phase 3 weights the two into WACC, and Phase 5 watches leverage kill banks and NBFCs in real cases.

Practice set

Pen, paper, basic calculator. Write your full answer before reading any solution, as working agreement #3 asks. Problems 1 to 3 are guided. Problems 4 to 9 are independent, and 10 is timed.

Problem 1 (guided). Asha can produce 4 chairs or 20 loaves of bread per week. Bharat can produce 1 chair or 10 loaves. (a) If each spends half the week on each good, what is total output? (b) Asha spends 75% of her week on chairs and 25% on loaves, and Bharat makes only loaves. Total now? (c) Bharat wants a chair. Making it himself costs him 10 loaves of production, and Asha will sell one for 7 loaves. Who gains?

Solution. (a) Asha makes 2 chairs + 10 loaves and Bharat 0.5 + 5, for a total of 2.5 chairs + 15 loaves. (b) Asha makes 3 chairs + 5 loaves and Bharat 10 loaves, for 3 chairs + 15 loaves. That's half a chair more and the same bread, purely from reallocating hours, because Asha gives up 5 loaves per chair and Bharat 10. (c) Both gain. Bharat pays 7 loaves for what would cost him 10, saving 3. Asha receives 7 for what costs her 5, gaining 2. Trade created 5 loaves of value from thin air, split between them. Businesses institutionalize this, and profit is the kept slice of created value.

Problem 2 (guided). A bakery needs ₹10 lakh to open. Option 1: borrow at 10%. Option 2: sell a 25% stake for ₹10 lakh. Compute the founder's income under each option, ignoring taxes, in (a) a good year with operating profit of ₹3,00,000 and (b) a bad year with ₹50,000. (c) What does the lender get in the good year? (d) Which claim is riskier for the outside money, and which for the founder?

Solution. Interest = ₹1,00,000/yr. (a) With debt, 3,00,000 − 1,00,000 = ₹2,00,000, and she still owns 100%. With equity, 75% × 3,00,000 = ₹2,25,000. (b) With debt, 50,000 − 1,00,000 = −₹50,000, so she must find the cash or default. With equity, 75% × 50,000 = ₹37,500, and the investor absorbs their share of the pain. (c) ₹1,00,000, never more, however great the year. (d) For outside money, equity is riskier. It has no floor and is paid last, so equity demands higher returns than debt, and that demand is the seed of every hurdle rate in the course. For the founder, debt is riskier, because fixed claims can kill. Equity shares the pain but also permanently shares every future upside. Neither is "better". They're different claims, priced differently.

Problem 3 (guided). Vistara Foods Ltd (synthetic) has 10 crore shares outstanding and earned ₹500 crore of net profit, and it pays out 30% as dividends. You own 10,000 shares. Compute (a) your ownership fraction, (b) EPS, (c) your look-through share of the profit, (d) dividend per share and the cash you receive, and (e) at a share price of ₹1,000, the P/E and the earnings yield.

Solution. (a) 10,000 ÷ 10,00,00,000 = 0.0001 = 0.01%, one part in 10,000. (b) EPS = ₹500 cr ÷ 10 cr shares = ₹50. (c) 0.01% × ₹500 cr = ₹5,00,000, equivalently 10,000 × ₹50. The business earned this for you whether or not it mailed any of it to you. (d) Dividends = 30% × 500 = ₹150 cr → DPS = ₹15, so you receive 10,000 × 15 = ₹1,50,000 in cash. The other ₹3,50,000 of your look-through profit was retained and reinvested on your behalf. Whether that's a gift or a slow leak depends entirely on the reinvestment ROIC versus the hurdle, which is question 3 meeting question 2 again. (e) P/E = 1,000 ÷ 50 = 20×, and earnings yield = 50 ÷ 1,000 = 5%. The earnings yield is the P/E upside-down, and a first bridge between prices and the return language used here.

Problem 4. Three synthetic firms face a 12% hurdle. Alpha: after-tax operating profit ₹24 cr on ₹150 cr invested capital. Beta: ₹33 cr on ₹300 cr. Gamma: ₹9 cr on ₹50 cr. (a) Compute and rank the ROICs. (b) Which create value? (c) Compute each economic profit in ₹ crore. Does the ROIC ranking match the rupees-of-value ranking?

Solution. (a) Alpha 24/150 = 16%, Beta 33/300 = 11%, Gamma 9/50 = 18%, so the ranking is Gamma > Alpha > Beta. (b) Gamma and Alpha clear 12%. Beta destroys value (11% < 12%). (c) Alpha (16−12)% × 150 = +₹6.0 cr, Beta (11−12)% × 300 = −₹3.0 cr, Gamma (18−12)% × 50 = +₹3.0 cr. The rankings don't match. Alpha creates the most rupees despite Gamma's higher ROIC, because it runs a decent spread over three times the capital. ROIC measures the machine's quality, and economic profit measures quality × size. A Gamma that can grow to Alpha's size at 18% is the holy grail, spread plus reinvestment room.

Problem 5. Kimaya Infra (synthetic) earns 7% ROIC on ₹200 crore of invested capital; hurdle 12%. Management announces a plan to double invested capital at the same return. (a) Compute profit and economic profit before and after. (b) Capitalized at the hurdle, what is each ₹100 of new capital worth once inside? (c) Write the one-sentence memo to the board.

Solution. (a) Before, profit is ₹14 cr and economic profit = −5% × 200 = −₹10 cr. After, profit has doubled to ₹28 cr, and economic profit = −5% × 400 = −₹20 cr, so destruction doubled too. (b) ₹100 yields ₹7/yr, worth 7 ÷ 0.12 = ₹58.3, so each new ₹100 becomes ~₹58 on arrival. (c) "Until returns exceed the cost of capital, every rupee of growth makes the owners poorer. Fix the 7% before feeding it." Politer variants are fine. The arithmetic isn't negotiable.

Problem 6. Compute ROIC as margin × turns and give a verdict versus a 12% hurdle: (a) Firm P, after-tax margin 6%, capital turnover 3.0×; (b) Firm Q, margin 15%, turnover 0.6×; (c) Firm R, margin 2.5%, turnover 6.0×. (d) Which most resembles the DMart/Costco pattern?

Solution. (a) 6% × 3.0 = 18%, which creates value with a +6% spread. (b) 15% × 0.6 = 9%, which destroys value despite the fattest margin (−3%). (c) 2.5% × 6.0 = 15%, which creates value (+3%). (d) R. Penny margins with ferocious turns are the discount-retail signature. Never read a margin without asking what turnover multiplies it.

Problem 7. A stable shop produces ₹2,00,000/yr, flat; your hurdle is 12%. Three quotes: (a) ₹10 lakh (b) ₹18 lakh (c) ₹25 lakh. Compute the implied yield at each price; which meet the hurdle? For those that don't, what would have to be true?

Solution. Implied yield = 2,00,000 ÷ price. (a) 20%, which clears easily. At your hurdle the shop is worth 2L ÷ 0.12 ≈ ₹16.7L, so ₹10L offers a wide margin of safety. (b) 11.1%, which just misses and is justified only by modest, durable growth. (c) 8%, well below. It requires meaningful dependable growth, or a much safer stream than assumed. Notice that the price didn't change the shop. It changed what must be true, and naming that is question 5's whole job.

Problem 8. Tag each observation with the primary five-questions number it informs. Overlaps exist, so pick the center of gravity. (a) "68% of revenue comes from one customer." (b) "The promoter has pledged 45% of their shares to lenders." (c) "ROCE has exceeded 25% for ten straight years." (d) "The stock trades at 90× earnings." (e) "60% of revenue is recurring subscriptions; 40% one-time hardware." (f) "CEO bonus is tied to revenue growth alone." (g) "A new technology could make the flagship product obsolete within a decade." (h) "The company reinvests ~all profits into new stores earning ~20% returns." (i) "At today's price, the company must grow 25%/yr for 15 years to justify it." (j) "Gross margin is 14%, but inventory turns 13× a year."

Solution. (a) Q4, because concentration is fragility. It also colors Q1. (b) Q3, promoter alignment, since pledged shares can force sales and desperate decisions. It feeds Q4. (c) Q2, durable high returns, the moat's fingerprint. (d) Q5, because a price implies a future. (e) Q1, the revenue model itself. (f) Q3, incentive design, since growth-only pay invites Busy-Ltd behavior (Problem 5). (g) Q4, existential threat mapping. (h) Q2, reinvestment at a spread, with Q3 credit to management. (i) Q5, expectations made explicit. (j) Q2, margin × turns quality evidence with a Q1 flavor. Ten scattered facts sorted themselves. The five questions are a filing system for everything you'll ever learn about a company.

Problem 9. Common-size walk (illustrative, ~FY24/FY25 scale). Fill the blanks. DMart, per ₹100 of revenue: cost of goods 85.3 → gross profit = ___; operating costs 6.8 → pre-depreciation operating profit = ___; depreciation 1.5 → operating profit = ___; interest & other (net) +0.3 → pre-tax = ___; tax 1.7 → net profit = ___. Costco, per $100 of total revenue: merchandise sales 98.1, membership fees 1.9; merchandise costs 87.4 → merchandise gross profit = ___; operating costs 9.1 → operating income (incl. membership) = ___; interest & other +0.2 → pre-tax = ___; tax 0.9 → net profit = ___. Then: (a) whose net margin is higher? (b) does that alone make it the better business, and what two things would you need before judging?

Solution. DMart: 100 − 85.3 = 14.7, 14.7 − 6.8 = 7.9, 7.9 − 1.5 = 6.4, 6.4 + 0.3 = 6.7, 6.7 − 1.7 = ₹5.0. Costco: 98.1 − 87.4 = 10.7, 10.7 + 1.9 − 9.1 = 3.5, 3.5 + 0.2 = 3.7, 3.7 − 0.9 = $2.8. (a) DMart, ~₹5.0 vs ~$2.8 per hundred. (b) No. You need (1) capital intensity and turnover, to convert margin into ROIC, which is the actual test, and (2) durability and price, meaning the spread's persistence (Q2/Q4) and what you're asked to pay (Q5). Margins start the conversation. They never end it.

Problem 10 (timed, 12 minutes, all six parts). (i) Define invested capital in one line. (ii) NOPAT ₹45 cr, invested capital ₹300 cr → ROIC? (iii) ROIC 10%, hurdle 12%, reinvesting heavily → value effect? (iv) Margin 3%, turns 6× → ROIC? (v) A stable ₹1,80,000/yr stream priced at ₹12,00,000: implied yield, and attractive against a 12% hurdle? (vi) Which of the five questions does "what growth rate is baked into today's price?" belong to?

Solution. (i) The money tied up inside the business so it can operate, regardless of whether debt or equity supplied it. (ii) 45/300 = 15%. (iii) It destroys value, because each rupee reinvested at 10% against 12% is worth ~83 paise and heavy reinvestment scales the loss. (iv) 3% × 6 = 18%. (v) 1.8L ÷ 12L = 15%, so yes, it clears 12%. At the hurdle the stream is worth ₹15L against a ₹12L price. (vi) Question 5. Scoring: 6/6 in time means you're fluent. Score ≤4 and you should redo the lemonade ledger and worked examples 2–3 before the mastery check.

Problem 11 (guided). Meghna Textiles (synthetic) has ₹250 crore of invested capital earning a 17% ROIC; hurdle 12%. (a) After-tax operating profit and economic profit today? (b) It reinvests ₹150 crore more at the same 17%; total economic profit now? (c) Capitalizing at the hurdle, how much value did that ₹150 crore create?

Solution. (a) Profit = 17% × 250 = ₹42.5 cr, and economic profit = (17 − 12)% × 250 = +₹12.5 cr/yr. (b) New capital is ₹400 cr, so economic profit = 5% × 400 = +₹20 cr/yr. (c) The ₹150 cr adds 17% × 150 = ₹25.5 cr/yr of profit. Capitalized, that's 25.5 ÷ 0.12 = ₹212.5 cr of value for ₹150 cr spent, so +₹62.5 cr is created. Equivalently, capitalize the ₹7.5 cr/yr of added economic profit: 7.5 ÷ 0.12 = ₹62.5 cr. A positive spread makes reinvestment a value engine, the mirror image of Problem 5.

Problem 12 (guided). A flat, dependable stream pays ₹4,00,000/yr; your hurdle is 12%. (a) The most you can pay and still meet the hurdle? (b) At an asking price of ₹40,00,000, the implied yield? (c) At ₹25,00,000? (d) Which prices clear the hurdle?

Solution. (a) 4,00,000 ÷ 0.12 = ₹33.3 lakh. (b) 4,00,000 ÷ 40,00,000 = 10%. (c) 4,00,000 ÷ 25,00,000 = 16%. (d) Only the ₹25 lakh price clears (16% ≥ 12%). At ₹40 lakh the 10% yield fails unless the stream grows dependably. The business didn't change between (b) and (c). Only the price changed, and with it what must be true to justify it.

Problem 13. Tag each observation with the single five-questions number it most informs. (a) Gross margin has held above 40% for twelve years despite three new entrants. (b) The statutory auditor resigned two weeks before results, citing "information delays". (c) The only manufacturing plant sits in a flood-prone district. (d) After a 30% price fall, managers bought ₹50 crore of stock with their own money. (e) The stock trades at 5× earnings while peers trade at 18×. (f) 70% of profit depends on a subsidy the government renews each year. (g) Customers would need ~18 months to requalify a competing supplier. (h) At today's price, a buyer needs 20%/yr cash-flow growth for twelve years just to break even.

Solution. (a) Q2, since a durable spread is the fingerprint of a moat. (b) Q3, because an auditor exit is a first-order honesty signal. (c) Q4, single-point physical fragility. (d) Q3, since insider buying with personal money is alignment made visible. (e) Q5. A low multiple is an implied expectation, here of decline, to be tested before anyone trusts it. (f) Q4. Renewal and policy dependence is an existential risk. It colours Q1 too. (g) Q2, since switching costs are a moat source. (h) Q5, the price's baked-in future, stated explicitly. Every fact you'll ever read about a company files under one of the five headings.

Problem 14. Two synthetic firms, hurdle 10%. Nadi Ltd: ₹800 crore invested at 14% ROIC. Setu Ltd: ₹800 crore at 7%. Each reinvests an extra ₹200 crore at its own ROIC. (a) Each firm's NOPAT before the reinvestment? (b) The added economic profit per year from the ₹200 crore? (c) Capitalized at the hurdle, the value created or destroyed by that ₹200 crore? (d) Both grew capital 25%. Which grower is richer, and why?

Solution. (a) Nadi 14% × 800 = ₹112 cr, and Setu 7% × 800 = ₹56 cr. (b) Nadi (14 − 10)% × 200 = +₹8 cr/yr, and Setu (7 − 10)% × 200 = −₹6 cr/yr. (c) Nadi's 8 ÷ 0.10 = +₹80 cr created, and Setu's −6 ÷ 0.10 = −₹60 cr destroyed. (d) Nadi. Identical 25% capital growth made its owners ₹80 cr richer and Setu's ₹60 cr poorer. Growth multiplies the sign of the spread, and it does nothing more.

Problem 15. Sundaram Auto (synthetic): 8 crore shares, ₹320 crore net profit, pays out 40% as dividends and reinvests the rest at a 16% ROIC (hurdle 12%). You own 5,000 shares. (a) EPS? (b) Your look-through share of this year's profit? (c) Dividend per share and the cash you receive? (d) Your retained-on-your-behalf amount? (e) Was the retention good for you, and by how much value per rupee retained?

Solution. (a) EPS = 320 ÷ 8 = ₹40. (b) 5,000 × 40 = ₹2,00,000, and the business earned this for you, distributed or not. (c) DPS = 40% × 40 = ₹16, so cash = 5,000 × 16 = ₹80,000. (d) Retained per share = ₹24, so your share = 5,000 × 24 = ₹1,20,000. (e) Yes. Each ₹1 reinvested at 16% throws off ₹0.16/yr, worth 0.16 ÷ 0.12 ≈ ₹1.33, which is +₹0.33 of value per ₹1 retained. Your ₹1,20,000 became ≈ ₹1,60,000 of value, a ~₹40,000 gift from good capital allocation that you never saw as cash.

Problem 16 (timed, 12 minutes, all six parts). (i) Define economic profit in one line. (ii) NOPAT $72m, invested capital $480m → ROIC? (iii) After-tax margin 4%, capital turnover 4.5× → ROIC? (iv) Invested capital ₹600 cr, ROIC 9%, hurdle 13% → economic profit (with sign)? (v) A flat ₹5,40,000/yr stream is priced at ₹36,00,000: implied yield, and does it clear a 12% hurdle? (vi) A firm reinvests heavily at an ROIC exactly equal to its 11% hurdle. What happens to value?

Solution. (i) Economic profit = (ROIC − hurdle) × invested capital, the value created or destroyed after charging for the capital used. (ii) 72 ÷ 480 = 15%. (iii) 4% × 4.5 = 18%. (iv) (9 − 13)% × 600 = −₹24 cr/yr. (v) 5,40,000 ÷ 36,00,000 = 15%, so yes, it clears 12%. (vi) Nothing. At ROIC = hurdle, growth is value-neutral, and each rupee reinvested returns one rupee of value. Scoring: 6/6 in time means you're fluent. Score ≤4 and you should redo worked examples 1 and 5 and Problems 4–5 and 11 before the mastery check.

Applied mini-project

First contact: DMart and Costco, from the actual filings. Give it ~1.5 hours. The aim is familiarization. That means extracting and describing what's there. Judging can wait. The full guided read of an annual report comes later this phase, and Phase 1 makes every line meaningful.

1. Pull the two documents (both free). Costco: SEC EDGAR (sec.gov/edgar → company search) → "Costco Wholesale" (ticker COST) → filing type 10-K → latest. Find the Consolidated Statements of Income (Item 8). DMart: dmartindia.com → Investor Relations → Annual Reports (or the NSE/BSE company pages) → latest annual report → the Consolidated Statement of Profit and Loss. Use consolidated, not standalone, and note in your journal that you noticed there are two. The difference gets explained when consolidation arrives.
2. Extract by hand into a one-page table per company: total revenue, net profit ("Net income" or "Profit for the year"), and shares outstanding. For Costco, take net sales and membership fees separately, and find shares on the cover page or in the equity note (~440–445m). For DMart, shares are in the equity note (~65 crore), and verify that against the filing.
3. Compute: net margin and profit per share for each. Compare your margins to the illustrative ~4.5–5% and ~2.9% used above. Small differences are expected, and they teach you something, so note the actual numbers and the filing year.
4. Write question 1 in your own words, one paragraph per company: what it does, who pays, why the customer chooses it, where the profit actually comes from. For Costco, compute this year's membership fees as a fraction of operating income.
5. Write your curiosity ledger: three specific things you noticed and three specific things you don't yet understand. "What is 'deferred membership fees'?" is a perfect example, and the accounting phase answers it. Date it and file it, in a plain folder until the toolkit installs the knowledge system. These six lines seed your first permanent notes.

Scoring rubric (self-graded; pass ≥ 9/12):

Case Lab: run case CL-0.1 (The Two Lemonade Stands of Jodhpur) in the app's Cases tab: two tiny businesses with the same profit but different capital, walked through all five questions end to end.

Reading & resources

Do the two "this week" items. The rest are queued on purpose, so resist reading ahead of the tools you'll be given. It's tempting, and it rarely sticks.

• Zerodha Varsity, Module 1, "Introduction to Stock Markets," chapters 1–3 (zerodha.com/varsity) [Free] [Beginner]. This week. The why-markets-exist story in Indian terms; later chapters overlap with the capital-markets module, where they are assigned.
• Mike Piper, Accounting Made Simple, chapters 1–2 [Paid] [Beginner]. This week, and buy the book now, since it's the Phase 0–1 reading spine. It covers the accounting equation and the statements at bird's-eye level, which is enough to make the guided annual-report read comfortable.
• Warren Buffett, "An Owner's Manual" (berkshirehathaway.com, Governance section) [Free] [Beginner]. The owner-related business principles, and the partial-ownership frame from the person who has used it best. ~30 minutes.
• Benjamin Graham, The Intelligent Investor (Zweig-annotated edition), chapter 8 only [Paid] [Beginner→Intermediate]. Mr. Market in the original. The full book is Phase 6's spine. Chapter 8 belongs to week 1 of your life as an analyst.
• Ray Dalio, "How the Economic Machine Works" (economicprinciples.org, 30-min video) [Free] [Beginner]. Watch once for orientation. Phase 7 rebuilds it with rigor and its critiques.
• Aswath Damodaran, "Valuation in Four Lessons" (Talks at Google, YouTube, ~60 min) [Free] [Beginner→Intermediate]. Optional, and a masterclass in the price-versus-value distinction Phase 3 operationalizes.
• Primary filings for the mini-project: Costco's latest 10-K via SEC EDGAR (sec.gov/edgar); Avenue Supermarts' latest annual report via dmartindia.com → Investor Relations or BSE/NSE [Free] [Beginner]. These are your first primary sources, and from this week on they outrank every summary.
• Charlie Munger, "A Lesson on Elementary, Worldly Wisdom" (1994 USC speech), free online, including in the Stripe Press edition of Poor Charlie's Almanack (press.stripe.com) [Free] [Intermediate]. Optional inspiration now; studied properly in Phase 6.
• Going deeper. Michael Mauboussin, What Does a Price-to-Earnings Multiple Mean? (Morgan Stanley / Counterpoint Global, free PDF) [Free] [Intermediate]. It unpacks question 5, showing what a multiple encodes about expected growth and returns. Optional now, and natural just before Phase 3.
• Going deeper. Aswath Damodaran, ROIC & cost-of-capital data by industry (pages.stern.nyu.edu → "Data") [Free] [Intermediate]. Real cross-sector ROIC and hurdle numbers to calibrate the ROIC-versus-hurdle intuition against how actual industries earn.

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. What follows shows how a working analyst amplifies the same skill today. It adds to the hand method and never replaces it. (R1/R10)

AI-Augment this skill

{
  "skill": "The five questions as a filing system for everything you will ever learn about a company, the price-versus-value distinction, ROIC against a hurdle rate, economic profit, margin × turns, and capitalizing a flat stream forwards and backwards",
  "use": "This is week one, so the honest uses are narrow and the boundary matters more than the technique. Learn the boundary here and it protects you for seventy-nine more weeks. (1) SORTING, not answering. The five questions are a classification scheme, and Problems 8 and 13 are exactly that drill. Paste ten facts about a company and ask which of the five each one informs, then grade the machine against your own sort and argue with every disagreement — the arguments are where the taxonomy gets into your hands. (2) VOCABULARY. 'What does invested capital mean?', 'explain the difference between a fixed claim and a residual claim' — these are questions about *language*, which is what a language model is actually made of, and §4.2's debt-versus-equity distinction survives being explained four different ways. (3) THE QUESTION-4 PRE-MORTEM. Ask what could kill a business and you get a candidate list to go verify in the filings; you never get a finding. (4) TURNING A CLAIM INTO AN ARITHMETIC CHECK. 'Write me the formula that turns margin and capital turnover into ROIC, and the turnover a 4.75% margin needs to clear a 12% hurdle' is safe and checkable in one line. Under all four sits one line you can state in a sentence and apply in a second: a question about the METHOD is safe; a question about the COMPANY is not.",
  "tools": ["Chat assistants — Claude, ChatGPT, Gemini — for sorting facts into the five questions, for vocabulary, and for the question-4 pre-mortem", "Your spreadsheet or notebook (M0.04 installs both) — for every number, including the ones a chat window offers to compute for you", "The primary filings themselves — DMart's annual report via NSE/BSE or the investor-relations page, Costco's 10-K via SEC EDGAR — which is where the mini-project already sends you"],
  "prompt": "Here are ten facts about a company: <PASTE>. For each one, tell me which of these five questions it primarily informs — (1) what does it do and how does it make money, (2) is it a good business with ROIC durably above its cost of capital, (3) is it run by good, honest, aligned people who allocate capital well, (4) what can kill it, (5) what is the price implying — and give me one sentence of reasoning per fact. Where a fact plausibly belongs to two, say which two and which is the centre of gravity. Do not tell me whether the company is good, do not estimate any figure I have not given you, and do not add facts of your own.",
  "verify": "Two disciplines, and the first is absolute. NO NUMBER. §4.6 of M0.04 states the ban as policy; here is the mechanism behind it. A language model produces the most plausible continuation, not the true one, so a request for DMart's revenue returns a correctly-shaped number that may be a year stale, on the standalone basis when you needed consolidated, or simply invented — and it reads exactly like knowledge, which is what makes it worse than a blank. Two cases are worse still and both live in this module: small and mid-cap Indian companies are thinly represented in any training corpus, and anything published after the model's training cutoff cannot be known at all. Second discipline: run the sort BEFORE you look at the answer, for the same reason §4.5 puts question 5 last. A machine's confident classification becomes your anchor if you read it first, and the whole value of the exercise is that you had to decide.",
  "diy": "The gate is unaided. You state the five questions verbatim and in order; you compute ROIC as profit over invested capital and again as margin × turnover; you compute economic profit with its sign and say what the sign means; you capitalize a flat stream forwards (cash ÷ required return) and backwards (implied yield = cash ÷ price); and you explain why a faster grower can be worth less. Nothing in this callout is admissible in that room, and nothing in it is needed there."
}

Modern Data Analysis

By hand first. You computed Steady Ltd against Busy Ltd, GroceryMart against Aurum Jewels, the fate of one retained rupee at three different returns, and the leverage ladder, one arithmetic line at a time, on paper. Keep that. The arithmetic is four operations deep, and if you need a machine for it you won't catch a machine's mistake.

Today's workflow. At this scale there's no speed to gain. The gain is that the master idea stops being two cases and becomes a surface you can look at. Write the value rule as one function of (ROIC, hurdle, capital, reinvestment), evaluate it on a grid, and three things appear that a worked example can't show. The sign change at ROIC = hurdle becomes a visible boundary running through the whole grid. In a worked example it was only the moral of one story. The break-even turnover curve, the turns a given margin needs to clear the hurdle, turns "high margin is not the same as good business" from an assertion into a line you can put DMart and Aurum Jewels on either side of. And the answer's sensitivity to the hurdle becomes measurable. That matters more than it looks, because the hurdle is the one input here you aren't yet equipped to estimate.

Tools & sources (IN + US). Use numpy for the grid and pandas for the cross-section, plotted with matplotlib. In India, screener.in company pages give the ROCE trend and the ten-year profit-and-loss block. The NSE and BSE corporate-filings archives hold the DMart annual report the mini-project already has you download. The RBI's Current Rates panel and the 10-year G-sec yield (rbi.org.in, and the DBIE portal at data.rbi.org.in) supply the risk-free leg that Phase 3 builds the hurdle on top of. In the US, SEC EDGAR has Costco's 10-K, and the companyfacts API gives a decade of the operating-profit and capital lines in machine-readable form. FRED series DGS10 and FEDFUNDS give the same risk-free leg in dollars. Damodaran's "Return on Capital by Industry Sector" and "Cost of Capital by Industry Sector" tables at pages.stern.nyu.edu, refreshed each January, answer "against what?" They give the sector median that tells you whether a 20% return is remarkable or ordinary in that industry.

# The master idea as one function, not two cases — recomputed in-session (R3)
import numpy as np
val   = lambda roic, k: roic / k                 # value of Re 1 retained, capitalised at the hurdle
created = lambda roic, k, reinv: (roic - k) / k * reinv     # value created BY that reinvestment
print(f"{val(.20,.12)*100:.1f} {val(.09,.12)*100:.1f}",     # 166.7  75.0   <- worked example 5
      f"{created(.18,.12,500):+.1f} {created(.08,.12,500):+.1f}")   # +250.0  -166.7 <- worked example 2
# the same 50% growth, opposite signs; and the faster grower CAN be worth less:
print(f"{created(.18,.12,250):+.1f} vs {created(.08,.12,500):+.1f}")   # +125.0 vs -166.7
roic = np.array([.08, .10, .15, .18, .20])                  # the whole surface, one line
print(np.round(np.outer(roic, 1/np.array([.09,.12,.14])), 3))
m = np.array([.025, .0475, .05, .10, .15])                  # turns needed to clear a 12% hurdle
print(np.round(.12 / m, 2))                                 # 4.80 2.53 2.40 1.20 0.80

Verify. Prove the engine against the worked figures above before it goes anywhere near a real company, and do it in the order they were built. In worked example 5, ₹100 retained at a 20% ROIC becomes ₹166.7 of value and at 9% becomes ₹75.0, and it's value-neutral at 12%. In worked example 2, reinvesting ₹500 crore at 18% against a 12% hurdle creates ₹250.0 crore and at 8% destroys ₹166.7 crore, with both firms growing profit 50%. In worked example 3, GroceryMart's 5% margin times 4× turns is a 20% ROIC and +₹8 of economic profit. Aurum's 10% times 1× is 10% and −₹2. In worked example 6, the same $500m machine returns 12% on equity unlevered and 17% with $200m of 6% debt, and the gap collapses to one point at $40m of pre-tax operating profit. Problem 9's common-size walk comes to ₹5.0 and $2.8 per hundred. Worked example 1's pharmacy is ₹14,28,571 at 7%, ₹8,00,000 at 12.5%, a 6.25% implied yield at ₹16 lakh, and ₹14,00,000 once 5% growth is added. If your function reproduces all of those, it has understood the value rule. If it misses one, fix the function and never the lesson.

Quantitative lens

Three results the lesson poses and cannot settle on paper. All of them are exact. No simulation runs here, and there is nothing to be uncertain about except the inputs, which is itself the point of the first finding.

The number you cannot yet compute matters more than the one you can. Value per rupee retained is ROIC ÷ hurdle, so the two partial derivatives are 1/k and −ROIC/k², and their ratio is ROIC/k, the value multiple itself. At the Indian settings used here, a 20% ROIC against a 12% hurdle, one percentage point of extra ROIC adds 0.083 of value per rupee retained while one percentage point of extra hurdle removes 0.139. Per point, the hurdle is 1.67 times as powerful as the return everyone argues about. At US settings, 20% against 9%, it's 2.22 times.

Put the stated hurdle ranges through it and you'll see the size. The same 20% business turns a retained rupee into ₹1.667 at a 12% Indian hurdle and ₹1.429 at 14%, a 14.3% swing from a 2-point range, and in the US the 8-to-10% range is a 20.0% swing. That's the case for Phase 3, made in advance. WACC gets its full treatment there because it's the highest-leverage input in the whole chain, and the one an analyst is most tempted to wave at. Its intellectual interest is beside the point. Until then, "hurdle" is a placeholder carrying more weight than it looks.

Margin and turns are equally important, and this can be proved. ROIC = margin × turns is multiplicative, so the elasticity of ROIC with respect to each is 1, verified numerically above at 1.000000 both ways. A one percent relative improvement in margin and a one percent relative improvement in turnover produce the identical improvement in return on capital. What differs is the cushion, and the cushion is what the eye reads wrongly. Against a 12% hurdle, a 4.75% margin needs 2.53× turns and a 10% margin needs 1.20×. DMart runs eleven to fourteen inventory turns against a 2.53 requirement, while Aurum Jewels runs 1.0 against a 1.20 requirement and fails. The fat-margin business is the one in danger. That makes "high margin equals good business" worse than a rough heuristic that sometimes misfires. It's a claim about half of a product, and the half it ignores has equal weight.

Growth is a multiplier on a sign, and the sign is the only thing that changes the answer's direction. created = (ROIC − k)/k × reinvestment is linear in the amount reinvested and changes sign only at ROIC = k. So the master idea is arithmetic. Steady reinvesting ₹250 crore at 18% creates ₹125.0 crore, while Busy reinvesting twice as much at 8% destroys ₹166.7 crore. Twice the growth, opposite direction. No amount of reinvestment converts a negative spread into value, and no amount of restraint converts a positive one into destruction.

Now the limits, and they're large enough that the three results above are best read as statements about the model. They say nothing about any company. The function holds ROIC constant when reinvestment is added, which no real business does. The marginal return on the next rupee is almost always lower than the average return on the rupees already inside, and the whole of Phase 4 exists because the interesting question is how long a spread survives being attacked. The function also holds the hurdle constant when a business levers up, and both the numeracy bootcamp and the later risk-and-return work will tell you that's false. It capitalizes a flat perpetual stream, the simplest object in valuation and the first thing the valuation phase complicates. And it says nothing whatsoever about whether a given company's reported ROIC is real. The numerator and denominator are both accounting constructions that Phase 1 teaches you to build and Phase 2 teaches you to distrust. The engine shows you the shape of the value rule, and the shape is all it shows.

Do it in code: write the function, evaluate it on a grid, put the six worked examples in as tests, and re-run the hurdle sensitivity with the range you would defend in place of the 12% handed to you here. Then go and get the real ROIC from a filing, which is the part no function does for you.

Where this goes next: galaxy cross-links

• Failure modes, verification and the primary-source guardrail (AI0.06, the crown of the AI branch). The full version of the method-versus-company boundary drawn above: which questions a language model can be trusted with, which it can't, and the verification routine that stands between them.
• How modern AI actually works (AI0.01). Why "plausible, not true" describes the mechanism and is no complaint about it, and so why the number ban is structural. It won't go away as the tools get better.
• Probability, distributions, sampling and estimation (QM1.01). A hurdle rate is an estimate with a distribution around it. There "12%" acquires an interval, and you learn what an interval obliges you to do.
• Issue trees and MECE (CN1.01). The five questions are a decomposition, and MECE is the method that says when a decomposition is exhaustive, when it overlaps, and how to build one for a problem nobody has handed you five questions for.
• pandas I, data wrangling (DA1.02). One company's ROIC is an anecdote. The same calculation across a sector, joined to a benchmark table, is evidence. The pandas library turns that second job into a routine.

Teach it back & journal

Feynman prompt. Write a one-page explainer for a smart 15-year-old titled "How a company can grow bigger every year and be worth less every year." The rules are short. Use no jargon, though you may use "return" and "hurdle" once you've defined them with a lemonade stand. Include one worked number example of your own invention (not Steady/Busy) and one real-world sentence about DMart or Costco. If your explainer can't survive the 15-year-old asking "but profits went UP, how is that bad?", rewrite until it can.

Journal reflection. Your journal can be a plain notebook until the toolkit installs something better. Write four things, dated. (1) Why you're doing this, in the plain three-sentence version you'd want read back to you in week 80. (2) Your diagnostic score by section, your placement decision, and the rubric rule that produced it. (3) The one idea from this week that most rearranged something you thought you understood, and one place in your own life where you can already see the ROIC-versus-hurdle logic operating: your employer, a shop you love, your consulting work. (4) The five questions and the master sentence, copied out by hand. You'll write them again from memory on Sunday. The gap between the two attempts is your first spaced-repetition datapoint.

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