Corporate Issuers & Equity-Market Completions

Branch: Economics & Corporate Completions (Finance-Plus Ring) · Node EC1.02 · ~20 hours · Standard mastery gate ≥85%

A company does not simply "have" a business; it also has to run the plumbing between that business and the people who fund it. Every day, cash is trapped in inventory and receivables and released, or not, by suppliers' patience. Every quarter, a board decides whether to send cash back to owners, and how, and the calendar around that decision has exact, checkable dates. Every time a share crosses a border, or a founder wants to keep control after selling most of the economics, the security itself has to be re-engineered, a receipt standing in for a share, a second class of stock with different rights attached. And every one of those decisions is judged against a benchmark whose construction, who's in it, how much each name is weighted, when it gets reshuffled, is itself a designed artifact with rules you can read. This module is the set of four "completions" that finish the corporate-issuer picture the rest of the program has been building: working-capital management, dividend-policy mechanics, equity security types, and index construction. None of the four is exotic. All four are the kind of precise, checkable, easy-to-get-subtly-wrong machinery that separates an analyst who sounds informed from one who actually is.

This Ring is additive institutional/CFA breadth, it presents the toolkit and the plumbing alongside, not in place of, the program's process-over-P&L, concentration-over-diversification philosophy. Nothing here asks you to trade on an ex-dividend date or chase an ADR arbitrage; it hands you the mechanics so that when a filing, a term sheet, or a benchmark provider's rulebook uses this vocabulary precisely, you are not guessing at what it means.

One flag before the content starts, because this module sits on a specific and under-appreciated fault line. Every one of its four completions is built from facts that are precise, dated, and change on a schedule, an ex-dividend date, a depositary ratio, a voting-rights fraction, an index-eligibility threshold, a tax section number. These are exactly the facts a fluent AI assistant will state with total confidence whether its training data is current or three years stale, because a confident wrong date reads identically to a confident right one (AI0.01's payoff line, applied here without exception). Worse, some of these facts changed recently and mechanically in ways an older mental model, human or machine, will get wrong with total sincerity: both India and the United States moved settlement from T+2 to T+1 in the last several years, and that single change silently altered a rule ("the ex-dividend date is one business day before the record date") that had been stable for decades. A model trained mostly on pre-transition text, or a colleague who last checked ten years ago, will state the old rule as fact. This makes corporate-actions and index mechanics one of the highest AI-over-trust surfaces in the corpus for a specific reason: unlike a hallucinated valuation multiple, there is no way to sanity-check an ex-date or a depositary ratio from first principles, you either know the current rule or you check a primary source, and this module is built to make you reach for the primary source by reflex.

Where it sits. M2.02 built the ratio toolkit: DIO, DSO, DPO, the Cash Conversion Cycle, and the current/quick/cash family. This module does not recompute a single one of those formulas; it starts exactly where M2.02 stops, at a CCC already measured, and asks what a treasury team actually does about it, with what instruments, at what cost. M3.07 built the value-creation math behind capital allocation, growth versus ROIC versus WACC, and the conservation-of-value test applied to a buyback. This module borrows only the tax-and-signaling layer of the dividend-versus-buyback choice and sends you back to M3.07 for the value arithmetic. AA1.03 built the full grammar of benchmark validity and the PRI-versus-TRI trap. This module's index-construction section is the supply side of that same benchmark: how the thing AA1.03 teaches you to validate actually gets built, weighted, and reshuffled, and leans on AA1.03 rather than repeating it.

Suggested hour budget. Core content 9h · worked examples 3h · practice set 4h · mini-project 2.5h · flashcards and mastery check 1.5h.

Learning objectives

By the end you can:

1. Manage, not merely measure, the Cash Conversion Cycle, name the specific operational lever behind each of DIO, DSO and DPO, classify a liquidity policy as matching, conservative or aggressive, and distinguish a drag on liquidity from a pull: building directly on M2.02's ratio computation without re-deriving it.
2. Compute the annualized cost of trade credit foregone under stated terms (e.g., "2/10, net 45"), and select among a short-term funding menu (bank line/cash-credit, commercial paper priced on a discount basis, and receivables factoring/supply-chain finance) on one consistent, all-in effective-annual-cost basis.
3. Reconstruct the mechanical anatomy of a dividend (declaration, ex-dividend, record and payment dates) including the T+1 settlement change that collapsed the ex-dividend date onto the record date in both India and the United States, and compute the frictionless theoretical ex-dividend price drop.
4. Compute the share-count and price arithmetic of a cash dividend, a dividend reinvestment (DRIP, including fractional-share handling), a bonus issue/stock dividend, and a stock split, and state precisely how a bonus issue differs from a split in what it does to reserves and par/face value.
5. Apply Lintner's partial-adjustment model to show why observed dividends are smoothed relative to swings in earnings, and connect dividend policy to signaling theory, the agency/free-cash-flow hypothesis, clientele effects and the tax-preference argument, including India's dated buyback-tax regimes (the October 2024 deemed-dividend rule and the April 2026 return to capital gains) and US (qualified-dividend holding-period) mechanics, each cited to its primary source.
6. Explain why depositary receipts exist, compute a cross-listing parity check from a real, verified depositary ratio, and state the mechanical difference between a sponsored and an unsponsored programme and between Levels I, II and III (ADRs) versus a GDR's typical listing venues.
7. Compute the gap between voting power and economic ownership created by a differential-voting-rights structure (India's historical DVRs and its newer superior-voting-rights framework for founders) and by a US dual-class structure, using a real, verified share-class ratio.
8. Build a small index from scratch: free-float-adjust a market-cap universe and compute constituent weights under cap-weighted, equal-weighted, price-weighted and a simple factor-tilt scheme on the identical universe, and quantify the turnover a rebalancing forces under each scheme.
9. Read a real index provider's published eligibility and reconstitution rules: NSE Indices' Nifty 50 methodology and S&P Dow Jones Indices' S&P U.S. Indices methodology, and screen a candidate company against them, cross-referencing (never re-deriving) AA1.03's seven benchmark-validity properties and its PRI-versus-TRI treatment.
10. Name, for each of the four completions above, the single fact most likely to be stale or fabricated in an AI assistant's answer, and the primary source that settles it.
11. (Productivity objective: R10.) Reproduce this module's cash-flow, weighting, and voting-power arithmetic in Python/pandas, and use an AI assistant to accelerate drafting and first-pass screening, while retaining the by-hand skill the mastery gate rewards and running every date, ratio, and rule through the Primary-Source Guardrail (Trace, Match, Recompute, Date-check, Cite) before it is used for anything.

The duality, stated once (R10). The gated skill is the arithmetic and the vocabulary, done and stated correctly by hand: an effective-annual trade-credit cost, a free-float weight, a voting-power gap. The productivity payoff is doing the same work over a thousand-line holdings file in fifteen lines of pandas. But this module's four completions are, individually and collectively, dominated by facts that are precise, dated, and perishable, and a fluent AI answer about any one of them is exactly as confident whether it is current or stale. Nothing here is drilled to nagging-caution levels for its own sake; it is drilled because this specific region of the corpus rewards a verify-first reflex more than almost any other.

Prerequisites & connections

Builds on. M2.02 supplies the entire ratio apparatus this module manages rather than re-derives: DIO, DSO, DPO, the identity CCC = DIO + DSO − DPO, the current/quick/cash ratios, and the "who finances whom" reading of a negative working-capital cycle (HUL, Costco, DMart). If any of those formulas is not automatic, that is M2.02's job, not this one's, this module begins exactly where M2.02 ends, at a CCC already correctly computed, and asks what a treasury team does about it. M3.07 supplies the five-uses-of-capital frame and the conservation-of-value proof that a buyback only creates value below intrinsic value: §2.5 below borrows only the tax-driven and signaling-driven layer of the dividend-versus-buyback choice and explicitly hands the value-creation arithmetic back to M3.07. Phase-4's moat modules (M4.04–M4.05) supply the sources of bargaining power that let a company run a negative or shrinking CCC without it being distress in disguise, §1 uses that vocabulary in passing (a business with real pricing power over its supply chain can stretch DPO for free; one without it is stretching into default) without re-deriving moat taxonomy. AA1.03 §9 supplies the seven benchmark-validity properties (specified in advance, appropriate, measurable, unambiguous, reflective of current opinion, accountable, investable) and the PRI-versus-TRI mechanics that §4.7 below leans on directly rather than repeating.

Explicit seams (read once, hold permanently). Three boundaries keep this module from silently duplicating a row it references. First: §1 teaches working-capital management (levers, funding choices, policy trade-offs) never the ratio arithmetic itself, which stays M2.02's. If you find yourself re-deriving what DSO is, you have wandered out of this module's lane. Second: §2.5 teaches the tax and signaling layer of the dividend-versus-buyback choice, never the value-creation math, which stays M3.07's; this module will tell you why a tax regime tilts the choice one way, never re-derive whether a buyback creates value at a given price. Third: §4 teaches index construction mechanics (how a benchmark is built, weighted and reshuffled) never benchmark validation, which stays AA1.03's; the moment a question becomes "is this a legitimate yardstick for this manager," you are in AA1.03's territory, not this module's.

Feeds forward. M3.09's modeling track consumes §1's short-term funding menu directly when a model needs a revolver-versus-CP financing assumption. Every Phase-5 sector playbook is, in effect, this module's §1 applied to one industry's specific working-capital shape. ES1.02 owns the full India/US/UK/EU regulatory map (SEC, SEBI, FCA) that governs disclosure around dividends, buybacks, and depositary programmes; this module owns the mechanics those regulators are regulating, not the regulatory architecture itself. The quant-code region's Data & Machine Learning branch takes the vectorised build of §4's weighting schemes (replicate an index in pandas over a real holdings file) as a direct extension of the arithmetic taught here by hand. Two nodes consume this module's output directly and are the natural next reads. AA1.08 takes the index construction of §4 and puts a wrapper around it: the exchange-traded fund as a legal and operating structure, the creation and redemption mechanism, tracking difference against tracking error, and the tracker's implementation costs, none of which are computed here. EC1.06 takes the dividend-policy baseline of §2.5 and builds the capital-structure theory on top of it, from Modigliani-Miller through the trade-off and pecking-order views to a target-structure decision, so the payout question and the leverage question end up answered in one frame rather than two.

The one-sentence version. Four completions to how a corporate issuer meets the equity market: how it manages the cash trapped inside its own operating cycle, how and whether it sends cash back to owners, what legal wrapper its shares wear when they cross a border or split into classes of unequal rights, and the published rulebook of the benchmark used to judge all of it.

Core teaching content

4. Index construction & benchmark mechanics

4.1 An index is a rules-based portfolio

Strip away the branding and an equity index is a portfolio built by a published rule, not a manager's judgment, a defined universe, a defined weighting scheme, a defined schedule for updating both. Four weighting philosophies dominate practice, and the choice among them is not cosmetic, it changes what the index measures:

• Market-capitalization weighting (specifically free-float-adjusted: §4.2), the dominant global convention (Nifty 50, the S&P 500, MSCI's country and regional indices). A stock's weight is proportional to the value of its shares actually available to trade, so the index's return tracks, by construction, what an investor holding the whole free-float market would have earned.
• Price weighting: the Dow Jones Industrial Average's legacy convention: weight is proportional to share price alone, regardless of company size. A $900 stock moves the index far more than a $40 stock with ten times the market cap, a genuine distortion, not a rounding quirk, and Worked Example 9 shows exactly how large it can be.
• Equal weighting: every constituent gets the identical weight, reset at each scheduled rebalance (e.g., the S&P 500 Equal Weight Index). This removes cap-weighting's "big stocks dominate" property, tilting toward smaller names, at the cost of forced, repeated trading to restore equal weights every time prices move apart, which §4.6 and Worked Example 9 quantify.
• Factor (smart-beta) weighting: weights are tilted by a chosen factor score (value, quality, low-volatility, momentum) on top of, or instead of, market cap, deliberately expressing a systematic bet rather than replicating the broad market.

None of these is "the" correct way to build an index, each is an internally consistent answer to "how much of this stock should the index hold," and the choice changes both the return series produced and, per AA1.03 §9, whether the benchmark is fair for a given strategy.

4.2 Free-float adjustment: why full market cap overstates what's actually investable

Full market capitalization is share price times total shares outstanding. Free-float market capitalization excludes shares not realistically available to ordinary investors, promoter/founder holdings, strategic stakes held by another corporate group, government holdings in a public-sector enterprise, and shares locked in under a regulatory or contractual restriction. The Investible Weight Factor (IWF) is the fraction (0 to 1) of full market cap that survives this exclusion: Free-float market cap = Full market cap × IWF. The logic: an index is meant to be a portfolio ordinary investors could actually replicate, and a share nobody can buy, because the promoter will never sell it, should not drive its weight or return the way a genuinely tradable share does. Both NSE Indices and S&P Dow Jones Indices publish detailed guideline notes on exactly how IWFs are computed and updated (NSE Indices' IWF guideline note; S&P's separate Float Adjustment Methodology document), the precise rounding conventions and exclusion categories are provider-specific, exactly the kind of granular, periodically-revised detail to read from the current guideline note rather than assume, this one included.

4.3 Real methodology, worked: NSE Indices' Nifty 50

NSE Indices' own Methodology Document for Equity Indices lays out the Nifty 50's construction with unusual precision, worth reading in its own words rather than a paraphrase. Eligibility draws from a defined universe, "constituents of the Nifty 100 index that are available for trading in NSE's Futures & Options segment", filtered by liquidity ("average impact cost of 0.50% or less during the last six months for 90% of the observations for a portfolio of ₹10 crores"), trading frequency ("100% in the last six months"), and size relative to the smallest existing constituent ("average free-float market capitalisation is at least 1.5 times the average free-float market capitalization of the smallest constituent in the index"). Maintenance runs on a fixed, mechanical clock: "the review of Nifty 50 is undertaken semi-annually based on data for six months ending January and July," with replacements "implemented from the last trading day of March and September," and "a four weeks' prior notice ... given to the market participants" before any change. Ad-hoc reconstitution outside this clock is reserved for genuine corporate events, mergers, demergers, delistings, not discretionary judgment calls. Source: NSE Indices' Methodology Document for Equity Indices, via nseindia.com/niftyindices.com, verify you are reading the current edition before relying on a specific threshold, since these documents are periodically revised.

4.4 Real methodology, worked: S&P Dow Jones Indices' S&P U.S. Indices (the S&P 500)

S&P's own methodology contrasts sharply with NSE's clockwork approach. The S&P 500 changes composition on an as-needed basis, with no scheduled reconstitution date, the document states plainly that "changes to index composition are made on an as-needed basis," with "index additions and deletions ... announced with at least three business days advance notice" (less at the Index Committee's discretion). This is a genuine philosophical difference from Nifty 50's fixed semi-annual clock: S&P 500 membership is a committee-supervised, mechanically-screened but discretion-retaining process; Nifty 50 membership is a scheduled, rules-mechanical process with a fixed calendar. (The broader S&P Total Market Index, which supplies the pool the S&P 500 draws additions from, does reconstitute annually and rebalance quarterly on a fixed schedule, it is the narrower flagship S&P 500 that runs on the as-needed cadence.) Eligibility is still screened mechanically: as of 1 July 2025, a US company needs a total market capitalization of at least US$22.7 billion (security-level float-adjusted market cap at least half of that threshold); a float-adjusted liquidity ratio (FALR) of at least 0.75; and (the screen with no Indian equivalent here) positive GAAP net income from continuing operations, both in the most recent quarter and summed over the trailing four quarters. Beyond the mechanical screen, the Index Committee retains explicit discretion, exceptions for spin-offs and acquisition-related additions, and consideration of overall GICS sector balance relative to the broader market. Source: S&P Dow Jones Indices, S&P U.S. Indices Methodology, verify the current edition and thresholds directly at spglobal.com/spdji before relying on a specific figure, since they are reviewed and adjusted periodically.

4.5 The same universe, four different index answers

Worked Example 9 builds a small, fully synthetic five-stock universe, computes each stock's weight under cap-weighting (free-float-adjusted), equal-weighting, price-weighting, and a simple factor tilt on the identical underlying five companies, then shocks one constituent's price to show what each scheme costs to rebalance. The point the exercise is built to make concrete: the weighting choice, not any difference in what the index holds, is often the single biggest driver of two indices' apparently different "views" on the same market.

4.6 Rebalancing versus reconstitution, and the turnover a weighting scheme forces

Reconstitution changes what is in the index, additions and deletions, governed by the eligibility rules in §4.3–4.4. Rebalancing changes constituent weights back toward a target, without necessarily changing membership. The two are frequently confused, and the weighting choice from §4.1 determines how much rebalancing-driven trading a tracking fund is forced into. A cap-weighted index is, in a precise sense, self-adjusting: if one constituent's price rises and another's falls, the index's own weights shift automatically in proportion, with zero trading required to "keep up", only genuine reconstitution or a periodic free-float update forces a trade. An equal-weighted index has no such property: the moment prices diverge, weights drift from equal, and the only way back is to sell the outperformers and buy the underperformers at the next scheduled rebalance, real, structural turnover a cap-weighted fund simply does not incur. Worked Example 9 quantifies this on the same Antariksh-5 universe: one large single-stock price shock forces zero required trading in the cap-weighted version and a specific, computable percentage of fund NAV in one-way turnover in the equal-weighted version, the structural reason equal-weight and other alternatively-weighted products typically carry higher transaction costs than a plain cap-weighted tracker.

4.7 Where this hands off to AA1.03

Everything in this section is about how a benchmark is built. Whether a given benchmark, once built, is a legitimate yardstick for a specific manager or mandate is a different question, and it is AA1.03 §9's, not this module's: the seven benchmark-validity properties (specified in advance, appropriate, measurable, unambiguous, reflective of current investment opinion, accountable, investable), the quantitative quality tests (coverage, turnover, the systematic-bias regression), and the Price Return Index (PRI) versus Total Return Index (TRI) distinction, where AA1.03 works out, with SEBI's January 2018 circular mandating TRI benchmarking for Indian mutual-fund schemes, exactly how much of a fund's apparent "alpha" against a dividend-blind PRI is nothing more than the dividend yield the PRI never counted. Read that treatment there; this module's job stops at how the thing gets built, not at whether it's fair to judge someone against it.

4.8 India versus US, side by side

{
  "skill": "Verifying an index's current eligibility rule or reconstitution date before relying on it",
  "use": "Use a document/research tool to pull the CURRENT methodology document directly from the index provider, rather than a secondhand summary, since these thresholds (market-cap floors, liquidity ratios) are reviewed and moved periodically.",
  "tools": ["Research/browsing-enabled assistants", "The index provider's own methodology PDF (niftyindices.com/nseindia.com for NSE Indices; spglobal.com/spdji for S&P DJI)", "A spreadsheet or short Python script to run the screen against a candidate's actual reported numbers"],
  "prompt": "Fetch the CURRENT methodology document for <INDEX>, published by <PROVIDER>, and extract: the eligibility thresholds (market cap, liquidity, any profitability screen), the reconstitution/rebalancing schedule and notice period, and the date the document itself was last revised. Quote the exact relevant passages rather than paraphrasing them.",
  "verify": "Confirm you are looking at the current edition - these documents carry a revision date and providers update them periodically (a market-cap threshold in particular is reviewed regularly). Recompute any eligibility screen yourself against the candidate company's own reported market cap, float, and liquidity data (Guardrail 1-5: Trace to the PDF itself, Match the date, Recompute the screen, Cite the document and its revision date).",
  "diy": "You must be able to compute free-float market cap, run a size/liquidity screen, and compute weights under each scheme by hand (Worked Examples 9-10) - what a document tool adds is currency on the exact thresholds, which move, not the mechanics, which don't.",
  "market": "US"
}

Modern Data Analysis, the Python/pandas way. Every computation here scales the same way once it leaves the page. The trade-credit and funding-cost comparisons in §1 are a five-line function applied down a pandas.DataFrame of quotes, one row per supplier or lender, sorted by effective annual cost. The weighting exercise in §4 is df['weight'] = df['ff_mcap'] / df['ff_mcap'].sum() for cap-weighting, 1/len(df) for equal-weighting, and a groupby-free one-liner for price-weighting, the point of Worked Example 9 is to make you distrust a library's default the moment it disagrees with your own hand computation, not to compute by hand forever. One trap specific to this territory: date arithmetic on corporate actions is deceptively easy to get wrong in code: pandas business-day offsets (pd.tseries.offsets.BDay) will happily compute an ex-date one business day before a record date, silently encoding the old T+2-era rule unless you explicitly branch on the settlement cycle in force on the date in question. A vectorised pipeline that is fast and wrong about a settlement rule is worse than a slow one done by hand, because the error is invisible in the output, the failure mode this module's opening paragraph warned about. The quant-code region's Data & Machine Learning branch is where the full index-replication and backtesting build lives; here, the point is knowing enough by hand to catch the library when it is confidently wrong.

Common mistakes & how experts think differently

1. Treating "manage the CCC" as "recompute the CCC." A novice re-derives DIO/DSO/DPO when asked how a company should improve its cycle; an expert has those numbers already and asks which specific, nameable lever (SKU rationalization, a credit-policy change, a supply-chain-finance programme) actually moves them, and at what cost.

1. Assuming a lower DSO or a higher DPO is always an improvement. Stretched too far, tightened too abruptly, either one costs more in lost sales or lost supplier goodwill than the cash freed is worth. M2.02's own "counterfeit negative working capital" checklist applies here with full force; the expert asks what the lever costs, not just what it frees.

1. Comparing financing quotes on their headline rate rather than an all-in effective-annual basis. A commercial-paper discount rate systematically understates the true cost of the cash actually raised (it is computed on face value, not proceeds); a factoring fee quoted "per 30 days" hides a much higher annualized number once the actual collection period is longer. Experts convert every quote to the identical basis before comparing anything.

1. Reciting "the ex-dividend date is one business day before the record date." This was true under T+2 settlement and is no longer true under the T+1 cycle now in force in both India and the US, where the two dates coincide. This is the single highest-value stale-fact trap in the whole module, and it is worth checking the current settlement cycle every time, not assuming.

1. Confusing a bonus issue/stock dividend with a stock split. Both produce identical shareholder-facing arithmetic (more shares, proportionally lower price, unchanged total value); only the bonus issue/stock dividend consumes reserves through an actual accounting entry. A company that has capitalized most of its free reserves through repeated bonus issues cannot keep doing so indefinitely; a split carries no such constraint.

1. Chasing an apparent ADR/GDR premium or discount as free arbitrage. The parity math (Worked Example 6) is simple; the frictions that keep a real gap from closing instantly (FX conversion, custody and conversion lag, and India's FEMA-governed two-way fungibility rules for ADRs/GDRs) are not simple, and a persistent gap is frequently the friction, not a mispricing an outsider can safely trade.

1. Assuming every differential-voting-rights structure runs the same direction. India's historical DVRs gave fewer votes (compensated by a higher dividend); India's newer SR shares and every US dual-class structure give founders more votes. Confusing the two, or assuming India only has one such mechanism, misreads the actual control structure in front of you.

1. Citing a specific company's DVR, dual-class terms, or depositary ratio from memory as a currently live fact. Tata Motors' DVR (for years the standard real-world Indian example) has since been converted into ordinary shares; a specific company's ratio or class structure can and does change. Verify against the company's own current disclosure or the exchange's current listing before citing a specific instrument as presently live.

1. Assuming market-cap weighting is simply "how an index works." The Dow Jones Industrial Average is price-weighted; equal-weight and factor-tilted products are widely used precisely because they deliberately reject cap-weighting's "big stocks dominate" property. The weighting scheme is a designed choice with real consequences (§4.5), not a fact of nature, and an equal-weighted index is not "passive" in the same sense a self-adjusting cap-weighted tracker is; it structurally requires real, repeated, computable rebalancing turnover (§4.6, Worked Example 9).

1. Assuming every index reconstitutes on the same kind of schedule. NSE's Nifty 50 runs a fixed, published semi-annual clock; the S&P 500 changes membership on an as-needed, committee-driven basis with no scheduled reconstitution date at all. Conflating the two mischaracterizes how either index actually behaves.

1. Ignoring free-float adjustment, or treating an Investible Weight Factor as permanently fixed. Using full market cap where free-float market cap is required overstates the weight of any company with large locked-in promoter, government, or strategic holdings; and a company's IWF itself changes when a promoter sells down, a lock-in expires, or a strategic stake changes hands, it is a periodically-updated input, not a constant.

1. Trusting an AI assistant's recollection of any of the above (a date, a ratio, a tax section, a threshold, an instrument's live status) without tracing it to the specific primary source. Every mistake on this list has a version that a fluent, confident, entirely-plausible-sounding AI answer will produce with zero visible hedge. This module's whole architecture exists to make "trace it to NSE/S&P/DTCC/IRS/the company's own IR page" the reflex, not the afterthought.

Worked examples

(All company names not identified as real are synthetic, invented for clean arithmetic, no real issuer implied. Figures marked "illustrative" for real companies are not asserted as live market data; check the current prices/rates before relying on them. Every number below was computed and checked in Python before being written here.)

Worked example 1: The cost of trade credit and a DPO renegotiation (India, ₹)

Rukmani Fabricators (synthetic) buys raw cotton yarn from a supplier offering terms of 2/10, net 45, a 2% discount for payment within 10 days, full amount otherwise due in 45 days. Rukmani's annual COGS runs ₹730 crore, evenly spread across the year, and its current DPO with this supplier is 30 days. Rukmani is considering a supply-chain-finance arrangement that would let it extend its DPO to 45 days without damaging the relationship (the supplier gets paid early by a bank, at the bank's rate, not Rukmani's).

Solution. Step 1, cost of the discount, if forgone. The float earned by skipping the discount is net period − discount period = 45 − 10 = 35 days. Effective annual cost of forgoing it: (0.02/0.98) × (365/35) = 21.28% (365-day basis; 20.99% on a 360-day convention). Even at the longer 45-day terms, skipping this discount is far more expensive than any of §1.5's funding menu. Rukmani should take the discount whenever it has the cash to do so.

Step 2, cash freed by the DPO extension. Daily COGS = ₹730 cr ÷ 365 = ₹2.00 cr/day. Extending DPO from 30 to 45 days (Δ = 15 days) frees 15 × ₹2.00 cr = ₹30 cr of cash, one time, as a permanent reduction in the working capital Rukmani must otherwise fund.

Step 3, what that ₹30 crore is worth. If Rukmani would otherwise have drawn that ₹30 cr on a cash-credit line at 9.5% per annum, the extension saves ₹30 cr × 9.5% = ₹2.85 cr of interest every year, indefinitely, a genuine, recurring saving, not a one-off.

Read it. Two separate levers, two separate numbers, and a clean hierarchy: paying to keep an early-payment discount (21.28% effective) is far more valuable than stretching DPO through supply-chain finance (₹2.85 cr/year on ₹30 cr, or 9.5%), which is itself far more valuable than doing nothing. An expert treasury team runs exactly this comparison before touching either lever.

Worked example 2: Financing $50 million for 90 days: the short-term funding menu, compared honestly (US, $)

Meridian Components Inc (synthetic) needs $50 million of seasonal working-capital financing for 90 days and is comparing three options.

Solution. (a) Revolving credit facility: SOFR (illustrative, 5.00%, check the current print at the New York Fed before relying on a level) + a 200 bps spread = 7.00% all-in. Interest over 90 days on an actual/360 basis: $50,000,000 × 7.00% × (90/360) = $875,000.

(b) Commercial paper, quoted on a discount basis at 5.30% for 90 days: discount amount = $50,000,000 × 5.30% × (90/360) = $662,500; proceeds actually raised = $50,000,000 − $662,500 = $49,337,500, this is the number the true cost must be measured against, not the $50 million face. Effective annualized cost on the proceeds actually raised: ($662,500 / $49,337,500) × (365/90) = 5.4458%. Add a 10 bps dealer fee and a 15 bps backstop-line cost (the standby bank facility a CP rating typically requires): all-in 5.6958%.

(c) Receivables factoring, on $50 million of invoices at a 90% advance rate (cash today = $45,000,000) and a fee of 1.75% per 30-day period, with an average 45-day collection period: fee = 1.75% × (45/30) = 2.625% of face = $50,000,000 × 2.625% = $1,312,500. Measured against the cash actually advanced ($45,000,000), the effective annualized cost is ($1,312,500/$45,000,000) × (365/45) = 23.6574%.

Read it. Ranked by all-in effective annual cost: CP 5.70% (cheapest, but requires strong enough credit to access the market) < RCF 7.00% < Factoring 23.66% (fastest and most collateral-light, but by far the most expensive per dollar actually advanced, and the option a company reaches for when the cheaper two are not available to it). The ranking would look completely different, and dangerously wrong, if you had compared the CP's 5.30% quoted discount rate directly against the RCF's 7.00% without first converting it to the same proceeds-based, fee-inclusive basis.

Worked example 3: Dividend dates, the ex-dividend drop, and a DRIP (India, ₹)

Deccan Consumer Products Ltd (synthetic) declares a ₹8.00 per-share cash dividend on a stock trading at ₹500 cum-dividend, under the current T+1 settlement cycle (so the ex-dividend date and record date fall on the same day, per §2.1). An investor holding 240 shares has opted into the company's DRIP, which offers new shares at a 2% discount to the ₹485 market price prevailing on the payment date.

Solution. Step 1, the ex-dividend drop. In the frictionless baseline, the price should fall by exactly the dividend amount: ₹500 − ₹10 = ₹490 (using a separate ₹10-dividend illustration to keep the arithmetic clean, for Deccan's own ₹8 dividend the identical logic gives a theoretical ₹492 ex-dividend price off a ₹500 cum-dividend quote). In practice the observed drop is rarely exactly the dividend amount, because dividends and capital gains are frequently taxed differently (§2.4's tax-preference friction) and because ordinary market noise on the day swamps a small, single-day theoretical adjustment, but the frictionless number is the correct baseline to reason from.

Step 2, the DRIP. Cash dividend = 240 shares × ₹8.00 = ₹1,920.00. DRIP reinvestment price = ₹485.00 × (1 − 2%) = ₹475.30. Shares purchased = ₹1,920.00 ÷ ₹475.30 = 4.0396 shares, 4 whole shares credited, with the 0.0396-share fractional remainder either carried forward as a fractional entitlement (the now-standard convention) or paid out as cash-in-lieu of 0.0396 × ₹475.30 ≈ ₹18.80.

Read it. Nothing about the DRIP created value out of nothing, the investor's own ₹1,920 dividend simply bought ₹1,920 (less the fractional remainder) of additional stock at a 2% discount to market, precisely the "not a bonus" point of §2.3.

Worked example 4: Lintner's smoothing model against a volatile earnings path (US, $)

Continental Foods Inc (synthetic) targets a 40% payout ratio and adjusts its actual dividend toward that target at a speed (adjustment factor) of 0.30 per year, meaning it closes 30% of the gap between last year's dividend and this year's target every year, rather than jumping straight to the new target. Its prior dividend was $1.20/share. EPS runs $4.00, then falls to $3.20 (a 20% drop), then recovers to $4.80 (a 50% jump).

Solution. Year 1: target = 40% × $4.00 = $1.60; new dividend = $1.20 + 0.30 × ($1.60 − $1.20) = $1.20 + $0.12 = $1.32.

Year 2: target = 40% × $3.20 = $1.28; new dividend = $1.32 + 0.30 × ($1.28 − $1.32) = $1.32 − $0.012 = $1.308.

Year 3: target = 40% × $4.80 = $1.92; new dividend = $1.308 + 0.30 × ($1.92 − $1.308) = $1.308 + $0.1836 = $1.4916.

Read it. EPS fell 20% between Year 1 and Year 2, yet the dividend fell only 0.91% (from $1.32 to $1.308), almost imperceptibly. EPS then rose 50% into Year 3, yet the dividend rose only 14.1% (to $1.4916), still well below the new $1.92 target. This is Lintner's smoothing exactly as the theory predicts: management protects the dividend from earnings volatility because a cut reads as a much stronger negative signal than a temporary earnings miss does on its own, and a company will absorb a genuine one-year earnings shock into retained cash rather than pass it straight through to the dividend.

Worked example 5: A share buyback under India's 2024 and 2026 tax regimes (India, ₹)

An individual investor bought shares of a listed Indian company at a cost basis of ₹200 per share and now tenders them into a buyback at a consideration of ₹500 per share. The investor sits in the 30% income-tax slab, is not a promoter, and has held the shares for more than twelve months. Compute the tax under the rule in force from 1 October 2024 to 31 March 2026, then under the rule in force from 1 April 2026.

Solution. Step 1, the 2024 rule, the dividend leg. Under Section 2(22)(f) of the Income-tax Act, 1961 (as amended by the Finance (No. 2) Act, 2024), the entire ₹500 consideration is deemed a dividend, taxed at the investor's slab rate: ₹500 × 30% = ₹150 of tax, regardless of what the shares originally cost.

Step 2, the 2024 rule, the capital-gains leg. Under the corresponding amendment to Section 46A, the consideration received is deemed nil for capital-gains purposes, the original ₹200 cost basis is not netted against the ₹500 received at all. Instead, the investor recognizes a ₹200 capital loss per share, available to carry forward and set off against other capital gains in future years.

Read it. The investor pays tax on the full ₹500 as if it were a dividend, and separately books a ₹200 loss that only has value if there is another capital gain to offset it against. Contrast this explicitly with the pre-October-2024 regime, under which the company bore a buyback distribution tax under Section 115QA and the shareholder received the ₹500 free of further tax in their own hands, the direction of who pays, and how, reversed with this single legislative change. Always confirm which regime is in force on the transaction date before relying on either calculation.

Step 3, the 2026 rule. A tender on or after 1 April 2026 is a capital gain: ₹500 − ₹200 = ₹300, taxed at 12.5% as a long-term gain on listed shares, ₹300 × 12.5% = ₹37.50 per share, before the ₹1.25 lakh annual exemption and cess, with no capital loss left over. A promoter tendering the same shares pays at the effective promoter rate instead: ₹300 × 22% = ₹66 for a domestic-company promoter, ₹300 × 30% = ₹90 for any other promoter. Read it. The same tender cost the non-promoter four times as much tax under the 2024 rule (₹150 against ₹37.50), which is why the date of the transaction decides the answer.

Worked example 6: Checking ADR parity, using Infosys's real, verified ratio (India/US, ₹/$)

Infosys's own investor-relations FAQ states a 1:1 ratio, one Infosys ADS on the NYSE represents exactly one equity share traded in India (a real, verified fact). Suppose (illustratively, not asserting a specific date's actual quote) Infosys trades at ₹1,850 on the NSE, the USD/INR rate is 83.50, and the NYSE-listed ADR quotes at $22.50.

Solution. Step 1, the fair (parity) value. Fair ADR price = (India price × ratio) / USDINR = (₹1,850 × 1) / 83.50 = $22.1557.

Step 2, the gap. Premium = ($22.50 − $22.1557) / $22.1557 = 1.55%, the ADR is quoted at a small premium to its India-parity value.

Read it. A 1.55% gap is small enough that transaction costs, currency-conversion costs, and the roughly one-business-day lag to actually convert between the receipt and the underlying share (subject to India's FEMA-governed two-way fungibility rules) can easily explain it without any genuine mispricing being present. The arithmetic is trivial once the ratio is known: 1:1 here, verified from Infosys's own disclosure, and the entire teaching point is that the ratio itself, not the arbitrage math, is the fact to verify before doing anything else with it, since it is exactly the kind of number that can be adjusted by an issuer over time.

Worked example 7: Dual-class voting power, using Berkshire Hathaway's real, verified ratios (US, $)

Berkshire Hathaway's own investor documentation states that one Class A share equals 1,500 Class B shares economically, but only 10,000 Class B shares' worth of votes.

Solution. Step 1: match the economics. 1,500 Class B shares carry the identical economic (dividend/liquidation) claim as 1 Class A share, by definition of the 1,500:1 ratio.

Step 2, but the voting power those 1,500 Class B shares carry. Each Class B share carries 1/10,000 of a Class A share's vote, so 1,500 of them carry 1,500/10,000 = 0.15 Class-A-equivalent votes, not the 1.0 vote a single Class A share carries for the same economic exposure.

Step 3, the power-per-dollar gap. Voting power per unit of economic value is 1.0 for Class A and (1/10,000)/(1/1,500) = 0.15 for Class B. The ratio: 1.0 / 0.15 = 6.667. A Class A share carries 6.67 times the voting power, per dollar of economic exposure, that a Class B share carries.

Read it. This is the mechanical essence of every dual-class structure, quantified precisely on a real, exceptionally stable, well-documented example: voting power and economic ownership are deliberately decoupled, and the ratio between them (not merely the existence of two classes) is the number that tells you how much control has been retained relative to capital raised.

Worked example 8: A synthetic DVR: voting power versus economic ownership, and the price discount (India, ₹)

Konkan Tyres DVR (fully synthetic, no real company implied) has 100 crore ordinary shares outstanding (1 vote each) and 20 crore DVR shares outstanding (1/10th of a vote each, a historically-informed ratio applied here to an invented company). The promoter holds 45 crore ordinary shares and no DVR shares. Ordinary shares trade at ₹800; DVR shares trade at an illustrative 15% discount.

Solution. Step 1: total votes. Ordinary: 100 cr × 1 = 100 cr votes. DVR: 20 cr × 0.10 = 2 cr votes. Total = 102 cr votes. Total economic shares (for ownership-share purposes) = 100 cr + 20 cr = 120 cr.

Step 2, the promoter's voting power versus economic ownership. Voting power = 45 cr ÷ 102 cr = 44.12%. Economic ownership = 45 cr ÷ 120 cr = 37.50%. Control leverage (voting % ÷ economic %) = 44.12% / 37.50% = 1.1765×, the promoter controls nearly 44% of the vote while owning just 37.5% of the economic pie, purely because the 20 crore DVR shares' votes are diluted to almost nothing in the denominator.

Step 3, the price discount. DVR price = ₹800 × (1 − 15%) = ₹680.

Read it. Unlike Berkshire's structure (Worked Example 7), where the super-voting class concentrates control in founders' hands, a DVR structure concentrates control in the hands of whoever holds the ordinary shares simply by diluting everyone else's votes, here, the promoter's ordinary-share stake alone is enough to hand it a control premium it did not pay for economically. Remember, from §3.5, that this specific arithmetic is illustrative of the mechanism; do not attach it to any specific currently-listed company without checking that company's own current voting structure.

Worked example 9: Four weighting schemes, one synthetic universe, and what a shock costs each to rebalance (India, ₹)

The Antariksh-5 Index (fully synthetic) consists of five invented companies:

Solution. Cap-weighted (free-float): each stock's weight is its FF market cap ÷ ₹248,700 cr total. Antariksh Bank 26.54%, Ganga Motors 27.02%, Himalaya Foods 16.28%, Konkan Energy 10.86%, Malabar Tech 19.30%.

Equal-weighted: every stock gets 1/5 = 20.00%, regardless of size.

Price-weighted (Dow-style): weight is each stock's price ÷ the sum of all five prices (₹7,500). Antariksh Bank 16.00%, Ganga Motors 32.00%, Himalaya Foods 8.00%, Konkan Energy 4.00%, Malabar Tech 40.00%.

Factor-tilted (illustrative value tilt): assign each stock a synthetic value score (Antariksh 1.3, Ganga 0.7, Himalaya 1.1, Konkan 1.4, Malabar 0.5), multiply each by its free-float cap weight, and renormalize to sum to 100%. Antariksh Bank 35.87%, Ganga Motors 19.67%, Himalaya Foods 18.63%, Konkan Energy 15.80%, Malabar Tech 10.03%.

Read it. Malabar Tech is the smallest company by free-float market cap of the three largest-priced stocks, yet it dominates the price-weighted index at 40% purely because it has the highest per-share price, the identical distortion that gives a small number of high-priced names outsized influence in the real-world, still-active Dow Jones Industrial Average. The value tilt moves weight sharply away from Ganga Motors and Malabar Tech (low value scores) and toward Antariksh Bank and Konkan Energy (high value scores), relative to the free-float baseline. Four defensible indices, one identical underlying universe, four different answers to "how much of this market should you hold."

Now shock it. Malabar Tech's price falls 50%, from ₹3,000 to ₹1,500 (all else unchanged). Step 1, the cap-weighted index. Its new FF market cap is ₹1,500 × 20 cr × 80% = ₹24,000 cr (down from ₹48,000 cr); new total FF market cap is ₹224,700 cr, so Malabar Tech's new weight is ₹24,000/₹224,700 = 10.68% (down from 19.30%). No trade was required, the new weight fell out automatically from the price move. Step 2, the equal-weighted fund. Take a ₹100 fund, ₹20 in each name before the shock. Malabar Tech's position falls with its price to ₹20 × (1,500/3,000) = ₹10; fund NAV falls to ₹20×4 + ₹10 = ₹90. Restoring equal weight requires each position to return to ₹90/5 = ₹18: sell ₹2 from each of the four unaffected names, buy ₹8 into Malabar Tech, one-way trading of (4×₹2 + ₹8)/2 = ₹8, or ₹8/₹90 = 8.89% of NAV, from this single rebalancing event alone.

Read it. The cap-weighted index absorbed the shock with zero required trading; the equal-weighted fund was forced into 8.89% one-way turnover at the very next rebalance, purely as a structural consequence of the weighting rule, not a judgment call, not new information, just arithmetic. A weighting scheme's "self-adjusting" property (or its absence) is a real, computable cost difference between products that both call themselves "passive."

Worked example 10: Screening a candidate against real, current eligibility rules (US/India, $/₹)

S&P 500 (US). A candidate company reports a total market capitalization of $24.0 billion and a float-adjusted liquidity ratio (FALR) of 0.82.

Solution. Against S&P's own published thresholds (S&P U.S. Indices Methodology, effective 1 July 2025): market cap must be ≥ $22.7 billion, the candidate's $24.0bn passes. FALR must be ≥ 0.75, the candidate's 0.82 passes. (Both screens passing is necessary, not sufficient, the profitability screen and the Index Committee's own discretion, including sector-balance considerations, still apply, and passing the mechanical screen is not itself an addition.)

Nifty 50 (India). A candidate's average free-float market cap over the trailing period is ₹44,000 crore; the current smallest constituent's average free-float market cap is ₹27,000 crore.

Solution. NSE's rule requires the candidate's average FF market cap to be at least 1.5× the smallest constituent's: 1.5 × ₹27,000 cr = ₹40,500 cr required. The candidate's ₹44,000 cr passes this specific screen (the liquidity/impact-cost and trading-frequency screens from §4.3 would still need to be checked separately).

Read it. Both screens are genuinely mechanical and genuinely computable from public disclosures, there is no excuse for guessing whether a company "probably" qualifies for either index when the actual threshold, and the actual reported number, are both available to check directly.

Practice set

Work each problem fully before reading its solution. All company names are synthetic unless stated otherwise; numeric answers are to about ±2% unless noted. Every solution below was verified in Python before being written.

P1 (guided). Trade-credit cost, different terms. A supplier offers "3/15, net 60." Compute the effective annual cost of forgoing the discount, on both a 365-day and a 360-day basis.

Solution. Float period = 60 − 15 = 45 days. 365-day basis: (0.03/0.97) × (365/45) = 25.09%. 360-day basis: (0.03/0.97) × (360/45) = 24.74%. Even at a longer 45-day float, this remains a very expensive discount to forgo.

P2. DPO stretch, different numbers. A company with annual COGS of ₹912.5 crore extends its DPO from 40 to 52 days. How much cash is freed, one time? If the alternative was a cash-credit line at 10.25%, how much annual interest is saved?

Solution. Daily COGS = 912.5/365 = ₹2.50 cr/day. Cash freed = (52−40) × ₹2.50 cr = ₹30.00 cr. Annual interest saved = ₹30.00 cr × 10.25% = ₹3.075 cr.

P3. Choosing the funding menu. A mid-sized company with no credit rating needs $10 million for 60 days. It cannot access the commercial-paper market. Which two items from §1.5's menu remain realistic options, and what is the single biggest determinant of which one it should choose?

Solution. A bank line/RCF and receivables factoring remain realistic (CP requires rating-agency-acceptable credit, which the company lacks by assumption). The determinant is the all-in effective annual cost of each, computed on a consistent basis (§1.5), factoring will typically be materially more expensive per dollar advanced, but may be the only option if the company also lacks unused bank-line capacity or acceptable collateral.

P4. Drags versus pulls. Classify each as a drag or a pull on liquidity: (a) a customer paying 45 days late; (b) a company routinely paying invoices the day they arrive, with no discount offered; (c) an unexpectedly reduced credit-line limit; (d) obsolete inventory that can only be sold at a steep discount.

Solution. (a) Drag (cash arriving too slowly). (b) Pull (cash leaving too quickly, with nothing gained for the early timing). (c) Drag (a liquidity source suddenly restricted). (d) Drag (an asset that should have converted to cash on schedule has not, and will convert to less cash than expected).

P5. Ex-dividend date under different settlement cycles. A company's record date is Thursday, 14 May. Under a T+1 settlement cycle, what is the ex-dividend date? Under the older T+2 cycle, what would it have been?

Solution. Under T+1: the ex-dividend date is the same day as the record date. Thursday, 14 May. Under the older T+2 cycle: the ex-dividend date would have been one business day before the record date. Wednesday, 13 May. This is exactly §2.1's stale-rule trap, worked as a direct date problem.

P6. DRIP, different numbers. An investor holds 500 shares of a company paying a ₹6.00/share dividend, with a DRIP offering a 3% discount to the ₹210 market price. How many whole shares are purchased, and what is the fractional remainder?

Solution. Cash dividend = 500 × ₹6.00 = ₹3,000. DRIP price = ₹210 × (1−3%) = ₹203.70. Shares purchased = ₹3,000/₹203.70 = 14.7276. 14 whole shares, fractional remainder 0.7276 shares (cash-in-lieu ≈ 0.7276 × ₹203.70 ≈ ₹148.24, or carried forward as a fractional entitlement).

P7. Bonus issue, different ratio. A company announces a 2:3 bonus issue (2 new shares for every 3 held). An investor holds 900 shares at ₹450 pre-bonus. Compute the post-bonus share count and theoretical price.

Solution. New shares per held = 2/3; post-bonus shares = 900 × (1 + 2/3) = 1,500 shares. Theoretical post-bonus price = ₹450 / (1 + 2/3) = ₹270. Check: 900 × ₹450 = ₹405,000; 1,500 × ₹270 = ₹405,000. Value conserved.

P8. Lintner model, a different adjustment speed. Using Continental Foods' Year 1 figures (EPS $4.00, target payout 40%, prior dividend $1.20) but a faster adjustment factor of 0.60 instead of 0.30, compute the new dividend, and explain what a higher adjustment factor means about management's smoothing philosophy.

Solution. Target = 40% × $4.00 = $1.60. New dividend = $1.20 + 0.60 × ($1.60 − $1.20) = $1.20 + $0.24 = $1.44: closer to the $1.60 target than the 0.30-speed case's $1.32. A higher adjustment factor means management closes the gap to the target payout faster, less smoothing, a dividend that tracks earnings more closely, and (by the signaling logic of §2.4) a policy that is more willing to let a genuine cut show through if earnings fall.

P9. India buyback tax, different numbers. An investor with a ₹350 cost basis tenders shares into a post-October-2024 buyback at ₹900, and sits in the 20% tax slab. Compute the tax on the deemed dividend and the capital loss recognized. Then recompute for a tender on or after 1 April 2026, the investor being a non-promoter who has held the listed shares for more than twelve months.

Solution. Entire ₹900 consideration is deemed dividend: tax = ₹900 × 20% = ₹180. Capital-gains consideration is deemed nil, so the entire ₹350 cost basis becomes a capital loss of ₹350, carried forward. Under the 2026 rule the gain is ₹900 − ₹350 = ₹550, taxed at 12.5%: ₹550 × 12.5% = ₹68.75, before the ₹1.25 lakh annual exemption and cess, with no capital loss.

P10. Qualified-dividend holding period. A US investor buys a stock 70 days before its ex-dividend date and sells it 10 days after the ex-dividend date. Does the dividend received qualify for preferential tax treatment?

Solution. Total holding period spanning the window = 70 + 10 = 80 days, comfortably more than the required 61 days within the 121-day window (60 days before through 60 days after the ex-date). Yes, it qualifies: assuming no risk-reducing positions (e.g., certain options or short sales against the position) interrupted the holding period, which the IRS's rule separately excludes from the count.

P11. ADR parity, a different ratio. A synthetic company "Coromandel Textiles" has an ADR ratio of 2 ADS : 1 equity share (i.e., each ADS represents half a share). Its India price is ₹640, and USD/INR is 84.00. What is the fair ADR price?

Solution. Each ADS represents 1/2 share, so fair ADR price = (₹640 × 0.5) / 84.00 = ₹320/84.00 = $3.81.

P12. Dual-class voting power, applied to a different structure. A synthetic company has a founder share class carrying 20 votes per share and an economic claim identical to the ordinary class (1 vote per share, 1 economic unit). Compute the founder class's voting power per unit of economic value, relative to the ordinary class.

Solution. Ordinary class: 1 vote / 1 economic unit = 1.0. Founder class: 20 votes / 1 economic unit = 20.0. Ratio: 20.0/1.0 = 20×, the founder class carries 20 times the voting power per unit of economic value that the ordinary class carries (a much larger multiple than Berkshire's 6.67×, illustrating that the size of the voting/economic gap is a designed choice that varies enormously across real structures).

P13. Index weighting, a 3-stock universe. Three stocks: X (price ₹100, free-float market cap ₹5,000cr), Y (price ₹400, free-float market cap ₹3,000cr), Z (price ₹200, free-float market cap ₹2,000cr). Compute each stock's weight under cap-weighting and price-weighting.

Solution. Total FF market cap = ₹10,000cr. Cap-weighted: X 5,000/10,000=50%, Y 3,000/10,000=30%, Z 2,000/10,000=20%. Total price = ₹700. Price-weighted: X 100/700=14.29%, Y 400/700=57.14%, Z 200/700=28.57%. Note the inversion: X is the largest company by free-float market cap but gets the smallest weight under price-weighting, purely because it has the lowest per-share price.

P14. S&P and Nifty eligibility, different candidate. A candidate has a total market cap of $21.9 billion and an FALR of 0.68. Does it pass the S&P U.S. Indices screen described in §4.4?

Solution. No. Market cap of $21.9bn is below the $22.7bn threshold (as of 1 July 2025), and FALR of 0.68 is below the 0.75 minimum. It fails on both counts independently, either failure alone would be sufficient to disqualify it from consideration.

P15. Ex-date and the qualified-dividend test, combined. A US investor's broker statement lists a stock's record date as 3 June, under the current T+1 cycle. The investor bought the stock on 20 May and sold it on 30 July. Identify the ex-dividend date and determine whether the dividend qualifies for preferential tax treatment.

Solution. Under T+1, the ex-dividend date equals the record date: 3 June. The 121-day qualifying window runs from 60 days before 3 June (roughly 4 April) through 60 days after (roughly 2 August). The investor held from 20 May to 30 July (entirely within the window, and for well over 61 days (over two months)) so the dividend qualifies, subject to no risk-reducing positions having interrupted the holding period.

Applied mini-project

Build and audit a corporate-issuer "completions" dossier.

Choose one real, currently-listed company in each of India and the US (or one company that is genuinely cross-listed via an ADR/GDR, covering both in one dossier) and produce a short, checkable dossier with four sections, mirroring this module's four blocks. Every specific fact you assert (a date, a ratio, a threshold, a tax provision) must be traced to a named primary source (the company's own investor-relations page, the relevant exchange, the relevant regulator, or the relevant statute) using the Primary-Source Guardrail (Trace, Match, Recompute, Date-check, Cite); nothing may be asserted "because an AI assistant said so."

Section 1: Working capital. From the company's most recent annual report, identify its DIO/DSO/DPO (recomputing them yourself, per M2.02, do not simply quote a screener's number) and write two to three sentences naming the specific lever(s) the company appears to be using to manage its cycle (a disclosed supply-chain-finance programme, a stated credit policy, a disclosed factoring arrangement), citing the specific note or disclosure you found it in.

Section 2: Dividend policy. Find the company's most recent dividend announcement and state all four dates precisely (declaration, ex-dividend, record, payment), confirming from the exchange's own notice whether the ex-date and record date coincide (as they should, under the current T+1 cycle in both markets) or diverge (which would itself be worth investigating). State whether the company operates a DRIP and, if so, its current discount (if any).

Section 3: Equity security type. If your company (or its cross-listed pair) has an ADR/GDR, state the current ratio directly from the company's own IR page or its most recent 20-F/annual report, and compute a parity check against a same-day quoted price on both exchanges. If the company has more than one share class, state the voting ratio and any sunset clause, citing the charter or listing prospectus.

Section 4: Index membership. State whether the company is a current constituent of a major index (Nifty 50, Nifty 100, S&P 500, or another named index), and if so, note its most recent free-float market cap and, if disclosed, its index weight. If it is not currently a constituent of an index it plausibly could qualify for, screen it against that index's current published eligibility thresholds (§4.3–4.4) and state which specific criterion it fails, if any.

Deliverable and self-check. One dossier, four sections, each fact cited to its specific primary source with the date you checked it. Score yourself: 2 points each for (a) Section 1's lever is specific and cited, not generic; (b) Section 2's four dates are stated correctly and the ex-date/record-date relationship is confirmed, not assumed; (c) Section 3's ratio or voting structure is traced to a current primary source, not a remembered figure; (d) Section 4's eligibility screen uses the actual current threshold from the provider's own methodology document; (e) every one of the four sections carries at least one explicit citation with a checked date. Pass at 8/10, with no zero on any item. This is the module's entire discipline compressed into one deliverable: nothing in any of the four sections may rest on an unverified recollection, yours or an AI assistant's.

Reading & resources

Everything below is an anchor to verify against and learn from, never a substitute for the company's or provider's own current primary-source disclosure.

Working capital and short-term financing:

• Your own company's annual report / 10-K notes on receivables, inventory, and borrowings, the primary source for any real DIO/DSO/DPO or funding-cost claim. [Free] [Beginner–Advanced]
• RBI's guidelines on the Trade Receivables Discounting System (TReDS) at rbi.org.in, the India-specific supply-chain-finance venue named in §1.5. [Free] [Intermediate]
• A standard corporate-finance text's chapter on short-term financial management (working-capital policy, the cost of trade credit) for the underlying theory this module applies. [Paid: most university corporate-finance textbooks] [Beginner–Intermediate]

Dividend mechanics and tax:

• DTCC's T+1 Dividend Processing FAQ (dtcc.com), the primary source for the ex-date/record-date relationship under T+1 in the US. [Free] [Intermediate]
• The Income-tax Act, 2025 (in force from 1 April 2026; Sections 2(40) and 69 carry the buyback rules) and, for earlier years, the Income-tax Act, 1961 (Sections 2(22), 46A, 194), via incometaxindia.gov.in, or a company's own investor-relations tax note (several Indian issuers publish plain-language buyback/dividend tax notes after each Finance Act change), the primary source for India's current dividend/buyback tax mechanics. [Free] [Intermediate–Advanced]
• IRS Instructions for Form 1099-DIV (irs.gov), the primary source for the qualified-dividend holding-period rule. [Free] [Intermediate]

Equity security types:

• A company's own investor-relations FAQ or 20-F filing (SEC EDGAR, for a US-listed foreign private issuer), the primary source for a current ADR/GDR ratio or share-class structure. [Free] [Beginner–Advanced]
• Berkshire Hathaway's own published Class A/Class B comparison document (berkshirehathaway.com), a real, stable, primary-source illustration of a dual-class ratio. [Free] [Beginner]
• SEBI's current ICDR Regulations (sebi.gov.in), the primary source for India's DVR and Superior Rights (SR) share provisions; confirm the currently effective version before relying on any specific threshold. [Free] [Advanced]

Index construction:

• NSE Indices' Methodology Document for Equity Indices, and its separate guideline note on Investible Weight Factors (niftyindices.com / nseindia.com), the primary source for Nifty 50's eligibility and reconstitution rules. [Free] [Intermediate–Advanced]
• S&P Dow Jones Indices' S&P U.S. Indices Methodology, and its separate Float Adjustment Methodology document (spglobal.com/spdji), the primary source for the S&P 500's eligibility rules and reconstitution philosophy. [Free] [Intermediate–Advanced]
• AA1.03 (this Ring), the full treatment of benchmark validity and the PRI-versus-TRI mechanics this module's §4.7 hands off to. [This program]

Do this, not just read: pull up your own broker's or a company's own investor-relations page for a dividend you have personally received, and check whether the ex-date matches the record date (it should, under the current T+1 cycle). Then pull the current NSE or S&P methodology document directly and find the one number (a market-cap threshold, a notice period) this module quoted, to confirm it is still current. Ten minutes of checking two primary sources will teach you more about this module's real discipline than another hour of reading about it.

Teach it back & journal

Feynman prompt. Explain to a colleague who has only ever heard "the ex-dividend date is one day before the record date" why that statement is now wrong in both India and the US, using nothing but the mechanics of T+1 settlement, no appeal to "the rules changed, trust me." Then, in the same breath, explain why a Berkshire Hathaway Class B share and a classic Indian DVR share both "have fewer votes than something else," yet represent structurally opposite ideas about who a reduced-voting instrument is designed to serve. If your colleague can, unprompted, predict that any specific company's DVR status, ADR ratio, or share-class terms should be checked against a current primary source before being relied on, rather than assumed to be permanently as described in a textbook or a chat assistant's answer, you have installed this module's actual lesson, which was never really about ex-dates or vote ratios themselves.

Journal prompt. Pick one real, currently-listed company you know reasonably well. Spend twenty minutes finding, from primary sources only, its most recent dividend's four dates, its ADR ratio (if it has one) or its share-class structure (if it has more than one), and its current index membership and free-float market cap. For each of the three facts, write one sentence on where exactly you found it and how you would re-verify it if asked to defend the number in front of a skeptical colleague. Then write a short paragraph on this: every one of this module's four completions (working capital, dividends, security types, index construction) is built from facts precise enough to be either exactly right or confidently wrong, with nothing in between and no way to tell which from the tone of the answer alone. Which single habit from this module, checking the settlement cycle before trusting an ex-date rule, tracing a ratio to the company's own IR page, or reading an index provider's methodology document directly rather than a summary of it, would most change how a colleague trusts your work, and what will you do this week to make it automatic?

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