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# Appendix C: Accounting and Financial Statements

*Appendices — Financial Economics: Claims, Prices, and Holders*

***

This appendix assumes you have never taken accounting. It assumes you have read §2.1, which is four pages, and nothing else. When you finish it you should be able to open a 10-K, find the three statements, check that they articulate, and compute the quantities the body of the book uses: book equity, book and market leverage, market-to-book, payout, interest coverage, free cash flow in each of the senses that phrase carries, and accruals.

It sits in a book about claims rather than a book about firms for the reason Chapter 2 opens with a balance sheet. **A balance sheet is a statement of claims.** Chapter 2 read the claim graph from the holder's side, asking who owns what; a firm's accounts read the same graph from the issuer's side, asking what has been promised and to whom. The right-hand side of a corporation's balance sheet is a list of the securities somebody in Chapter 2's master table is holding. Nothing here is a new idea; it is Chapter 2's directed graph of promises, written in the notation the promisor uses.

Three symbols are introduced here and used nowhere else: $$\mathrm{BE}$$, $$\mathrm{ME}$$ and $$\mathrm{BD}$$ for book equity, market equity and book debt. All three are roman, in the manner of NOTATION.md's other measured statistics, and the roman face is doing work — the italic $$E$$ and $$D$$ of Chapters 10, 22 and 23 are *market* values, and much of the confusion in leverage measurement comes from writing the two with one letter. §16.1's balance-sheet $$A$$ and $$E$$, and its leverage $$L = A/E$$, are used unchanged, as are roman abbreviations for line items: $$\mathrm{NI}$$, $$\mathrm{CFO}$$, $$\mathrm{EBIT}$$, $$\mathrm{Dep}$$, $$\mathrm{Capex}$$, $$\mathrm{Int}$$, $$\Delta\mathrm{NWC}$$.

***

## C.1 What a Balance Sheet Is

### C.1.1 The identity, and why it is an identity

A balance sheet lists what an entity owns and what it owes at an instant, and asserts

$$
\text{Assets} = \text{Liabilities} + \text{Equity}.
$$

This is an identity, not a hypothesis, and the distinction matters more than it looks. Equity is *defined* as assets minus liabilities. There is no independent measurement of it that could disagree. A balance sheet that fails to balance is an arithmetic error, never a discovery about the firm.

The machinery that enforces it is **double entry**: every transaction is recorded twice, once as a debit and once as a credit, in a way that preserves the identity. Buy a machine on credit and an asset and a liability rise together; sell goods at a profit and assets rise by more than liabilities, the difference landing in equity by way of the income statement. Luca Pacioli described the system in 1494; it has not needed amendment.

What the identity does *not* say is that the numbers are right. It says they are consistent. At what value each asset is carried is a separate question, and §C.1.3 is about the places where the answer is least satisfying.

The economic content is what §2.2 called seniority: the claims on a pool of assets exhaust the pool, every dollar is spoken for, and equity is whoever is last in the queue. A balance sheet is therefore a picture of a capital structure, which is what Part V is about. And it is a **stock**, photographed at a date; the income statement and the cash flow statement are the **flows** connecting two consecutive photographs — the relation the Financial Accounts' stock and flow tables have in §2.1, one entity at a time.

### C.1.2 Every line is somebody else's line

Table C.1 is a stylized nonfinancial firm's balance sheet with a column the standard presentation omits: who is on the other end.

**Table C.1: A firm's balance sheet, with the holder of each claim**

| Line                          | Side      | Real or financial | Who holds the other end                                          |
| ----------------------------- | --------- | ----------------- | ---------------------------------------------------------------- |
| Cash and equivalents          | Asset     | Financial         | A bank (as a deposit liability) and the Treasury (as bills)      |
| Accounts receivable           | Asset     | Financial         | Customers, who carry the identical amount as accounts payable    |
| Inventory                     | Asset     | Real              | Nobody. It is a thing                                            |
| Property, plant and equipment | Asset     | Real              | Nobody                                                           |
| Goodwill and intangibles      | Asset     | Neither           | Nobody — see §C.1.3                                              |
| Accounts payable              | Liability | Financial         | Suppliers, as receivables                                        |
| Long-term debt                | Liability | Financial         | Bond funds, insurers, pension funds, foreign holders (Ch 2 §2.3) |
| Pension obligation            | Liability | Financial         | Current and retired employees                                    |
| Common equity                 | Residual  | Financial         | Households, directly and through funds (Chs 14, 16, 17)          |

*Source: Author's construction*

Read the last column down and the appendix's organizing claim appears. The liability and equity side of the corporate sector's balance sheet **is** the asset side of Chapter 2's holdings tables. When the Financial Accounts report that mutual funds hold some trillions of corporate bonds, they are reporting the long-term debt rows of Table C.1, summed across issuers and sorted by holder; the Z.1's balance sheet of the nonfinancial corporate business sector (tables B.103 and L.103 in recent vintages) is this table, aggregated. One accounting system, read in two directions.

Goodwill is the row that does not fit: an asset with no counterparty, no physical existence and no cash flow of its own, which exists only because somebody paid more for a business than the fair value of its identifiable net assets and the system needed somewhere to put the difference.

### C.1.3 Book value against market value

**Book equity**, $$\mathrm{BE}$$, is total assets minus total liabilities as the accounting system measures them. **Market equity**, $$\mathrm{ME}$$, is the share price times shares outstanding. The ratio

$$
\frac{\mathrm{ME}}{\mathrm{BE}}
$$

is the market-to-book ratio of §22.2, and its reciprocal is the book-to-market ratio §6.2 sorts on to build HML. In the standard empirical construction, following Fama and French (1993) and Davis, Fama and French (2000), book equity is stockholders' equity plus balance-sheet deferred taxes minus the book value of preferred stock — worth knowing because it is not the number on the face of the balance sheet, and because firms with negative book equity are dropped from the sort rather than assigned an enormous ratio.

The system is **historical cost with modifications**: most assets enter at what was paid and are then depreciated, amortized or written down, never written up. The modifications are the fair-value ones, concentrated in financial assets. Three divergences do most of the damage.

**Intangibles.** Research and development, advertising, training and software development are expensed as incurred, so the asset they create — a drug pipeline, a brand, organizational capital — appears nowhere. If the same asset is *bought*, in an acquisition, it appears at the price paid, as identifiable intangibles and goodwill. Two firms with identical economics therefore report book equity differing by the whole value of the intangible, depending on whether they built it or bought it. Since 2002 goodwill is not amortized but tested annually for impairment, converting a slow drip into an occasional cliff: Chapter 22's opening episode, AOL Time Warner's roughly ninety-nine-billion-dollar loss in 2002, is that mechanism firing at once. As the capital stock has shifted toward intangibles (Lev and Gu 2016), $$\mathrm{BE}$$ has become a worse measure of invested capital — a candidate explanation for the value premium's absence after 2007 (Ch 6 §6.2), and part of why measured Tobin's Q has trended upward (Ch 22 §22.4).

**Long-dated debt.** Debt the firm has issued is carried at amortized cost — roughly, proceeds plus accrued discount — not at market. A firm that issued a thirty-year bond at three percent and now sees it trade at sixty cents still shows it at par: its *book* leverage has not moved, while its *market* leverage has fallen. The same asymmetry runs on the asset side for held-to-maturity securities, which is §C.4.2's subject.

**Marked positions.** Trading assets are carried at fair value with changes running through net income; available-for-sale securities at fair value with changes running through other comprehensive income, bypassing net income entirely. Fair value is not always a price: under the ASC 820 hierarchy (§C.5.2), Level 1 is a quoted price for the identical instrument, Level 2 a model with observable inputs, Level 3 a model with unobservable ones. A Level 3 fair value is an opinion held to a standard.

Two leverage ratios follow, and they are different dependent variables:

$$
\text{book leverage} = \frac{\mathrm{BD}}{\mathrm{BD} + \mathrm{BE}}, \qquad \text{market leverage} = \frac{\mathrm{BD}}{\mathrm{BD} + \mathrm{ME}}.
$$

§23.6 records Welch's (2011) two objections, both of the measurement kind this appendix exists to make legible. The widely used debt-to-assets ratio puts *non-financing* liabilities — payables, pension obligations, deferred taxes — in the denominator, so a firm that stretches its payables is recorded as having deleveraged when it has borrowed more, from its suppliers. And because $$\mathrm{ME}$$ moves far more than anything the firm does, a market-leverage regression is substantially a regression on past stock returns. Neither objection is fatal; both mean a leverage result must state which ratio it used.

### C.1.4 Consolidation, and what leaves the balance sheet

A balance sheet has an edge, and the interesting accounting happens at the edge. The governing principle: **consolidate what you control, show at one line what you influence, disclose what you neither control nor influence.**

**Subsidiaries** under the parent's control are consolidated line by line — the subsidiary's assets and its debts inside the parent's totals — with outside ownership shown as a non-controlling interest inside equity.

**Equity-method investments**, typically twenty to fifty percent stakes conferring significant influence, appear as one asset line, with the investor's share of the affiliate's earnings on one income-statement line. The affiliate's *debt* appears nowhere, so a firm can be economically levered through affiliates while reporting a clean balance sheet — and joint ventures in capital-intensive industries are structured with that in mind.

**Variable interest entities** are the securitization case Chapters 13 and 19 need. A sponsor consolidates a vehicle if it is the primary beneficiary — power over the activities that most affect the vehicle's economics, plus an obligation to absorb losses or a right to receive benefits. Before the rules were tightened after the crisis (effective 2010), many conduits left the sponsor's balance sheet while the sponsor retained a liquidity backstop. In 2007 and 2008 the backstops were drawn and the vehicles came back. An exposure off the balance sheet is not off the firm.

**Leases** are the cleanest example of a definitional break in a data series. Until 2019 an operating lease was disclosed in a footnote as a schedule of minimum future payments, which analysts capitalized by rule of thumb at around eight times annual rent. Under ASC 842 and IFRS 16 the lessee records a right-of-use asset and a lease liability on the balance sheet. Nothing about any airline or retailer changed in 2019; measured leverage jumped anyway. Any leverage panel spanning that date carries a break, and a cross-country comparison carries two, since the two standards classify the resulting expense differently.

***

## C.2 The Income Statement and the Cash Flow Statement

### C.2.1 Accrual against cash

**Accrual accounting** records revenue when it is earned and expenses when they are incurred, regardless of when cash moves. **Cash accounting** records both when money changes hands. The income statement is on the accrual basis, the cash flow statement on the cash basis, and the difference between them is §C.3.3's subject.

![Figure C.2: Accrual against cash](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-6bc03f58cf70787702ef3ec38cdc74269cc96c05%2Ffig_C_02_accrual_vs_cash.png?alt=media)

**Figure C.2: Accrual against cash.** One transaction, on the two bases the two statements use, against one time axis. The accrual basis books the whole forty of profit in November, when the goods shipped and the revenue was earned. The cash basis books a loss of sixty in October, when the inventory was paid for, and a profit of a hundred in January, when the customer paid. Neither is wrong; they are answers to different questions, and the difference between them is the accrual. What makes the picture worth drawing is where the fiscal year end falls. The firm reports forty of profit for a year in which its cash balance fell by sixty, and every number in both statements is correct. The gap is a receivable, and the reason analysts watch receivables grow relative to revenue is that this figure with the January bar removed — a sale recognized and never collected — looks identical to this one until the collection date arrives. *Source: Author's construction from Section C.2.1.*

Take one transaction. On 15 November the firm ships goods that cost it 60 to make, for a price of 100, on sixty-day terms. The inventory was bought and paid for in October. The customer pays on 14 January. The fiscal year ends 31 December.

**Table C.2: One transaction, two bases ($)**

|                         | Year 1  | Year 2  |
| ----------------------- | ------- | ------- |
| **Accrual basis**       |         |         |
| Revenue                 | 100     | 0       |
| Cost of goods sold      | 60      | 0       |
| Profit                  | **40**  | **0**   |
| **Cash basis**          |         |         |
| Cash received           | 0       | 100     |
| Cash paid for inventory | 60      | 0       |
| Cash profit             | **−60** | **100** |

*Source: Author's construction*

Both columns are correct, and over the two years they sum to the same 40. The accrual basis puts the profit in the period the firm did the thing that earned it; the cash basis puts it in the period the money arrived. For a firm in a steady state the two nearly coincide. For a growing firm — extending more credit and building more inventory each year — the accrual basis permanently reports profits the cash basis has not yet seen. That is the point of accrual accounting, not a defect, and it is also why a growing firm can be profitable and insolvent at once.

### C.2.2 Revenue recognition and the matching principle

Two conventions generate accrual accounting from that definition.

**Revenue recognition.** Under the standard effective for US public companies in 2018 (ASC 606, and its IFRS twin), revenue is recognized when control of the promised good or service transfers to the customer, in the amount the seller expects to be entitled to. The five-step apparatus behind that sentence exists because the hard cases are hard: multi-element contracts, licences, variable consideration, long-term construction. The residue for this book is that revenue is a *judgment about transfer of control*, not a record of a bank transfer, and a contestable judgment will sometimes be contested.

**Matching.** Costs are recognized in the period whose revenue they helped produce. Depreciation is the canonical device: a machine used for ten years is expensed over ten, so the cost sits alongside the revenue it generated. Every matching convention requires an estimate — useful life, the fraction of receivables that will go bad, the warranty claims a year's sales will generate, the percentage of a contract complete. Each estimate is a dial, turned by a manager whose pay depends on the number at the end.

That is what a reader needs in order to read an earnings surprise. §7.3's post-earnings-announcement drift runs in the direction of a *surprise* measured against an analyst consensus usually built on a non-GAAP number the company itself defines. Two firms with identical cash flows can report different earnings, legally, by turning different dials, and the distribution of reported earnings has a documented discontinuity at zero and at the prior year's level — too few small losses, too many small profits (Burgstahler and Dichev 1997). The market reacts to the reported number; whether it unpacks the accruals inside it is §C.3.3.

### C.2.3 The cash flow statement, and Chapter 25 in disguise

The cash flow statement sorts every movement of cash into three sections.

**Operating** covers cash generated by the business: collections from customers, payments to suppliers and employees, interest paid, taxes paid. Under the **indirect method**, which nearly every US filer uses, the section does not list those items. It starts at net income and undoes the accruals — adding back non-cash charges such as depreciation, subtracting the increase in non-cash working capital — so the presentation is a reconciliation rather than a list, arriving at the number the direct method would produce.

**Investing** covers purchases and sales of long-lived assets and of securities: capital expenditure, acquisitions, disposals.

**Financing** covers transactions with the holders of the firm's claims: debt issued and repaid, equity issued and repurchased, dividends paid.

That third section is Chapter 25's data source in disguise. It reports, firm by firm, the quantities the Financial Accounts report sector by sector — net equity issuance, net debt issuance, distributions to holders. §25.1's opening fact, that internal funds cover the large majority of corporate capital expenditure, is the operating section set against the investing section and aggregated; §23.4's market-timing evidence is built on the equity-issuance line. Watch the sign convention: a firm can show positive financing cash flow while paying a large dividend, if it borrowed more.

Payout measures come from here and the income statement together. Chapter 23's Lintner block writes the target payout ratio as

$$
\mathrm{POR} = \frac{\mathrm{Div}}{\mathrm{NI}},
$$

but dividends are no longer most of payout. **Total payout** adds repurchases; **net payout** subtracts equity issuance, which matters for firms repurchasing with one hand and issuing to employees with the other. §23.5's argument that a repurchase and a dividend are not equivalent commitments is about the two lines' different persistence, not their arithmetic.

### C.2.4 Free cash flow, in each of its senses

At least four distinct quantities are called free cash flow, and a valuation that mixes them is wrong by construction.

**Free cash flow to the firm** is the cash available to all claimholders, computed before financing:

$$
\mathrm{FCFF} = \mathrm{EBIT}(1-\tau\_c) + \mathrm{Dep} - \Delta\mathrm{NWC} - \mathrm{Capex}.
$$

**Free cash flow to equity** takes out what the lenders receive and adds what they lend:

$$
\mathrm{FCFE} = \mathrm{FCFF} - \mathrm{Int}(1-\tau\_c) + \Delta\mathrm{BD}.
$$

**Cash flow from operations minus capital expenditure** is what financial journalism means by free cash flow. It is neither of the above and stands in a fixed relation to the second:

$$
\mathrm{CFO} - \mathrm{Capex} = \mathrm{FCFE} - \Delta\mathrm{BD},
$$

because $$\mathrm{CFO}$$ is already after cash interest and cash taxes but before new borrowing. Section C.3.2 computes all three for one firm and gets 22.7, 59.0 and −1.0, which indicates how much the choice matters.

**Jensen's free cash flow** (Ch 24 §24.2) is a fourth thing: cash in excess of what is needed to fund all positive-net-present-value projects. It is a theoretical construct, not a line anyone computes.

§22.1's discipline is a matching rule. **Free cash flow to the firm is discounted at the weighted average cost of capital and produces enterprise value, from which net debt is subtracted to reach equity value. Free cash flow to equity is discounted at the cost of equity and produces equity value directly.** Discounting flows to equity at the WACC double-counts the tax shield; discounting flows to the firm at the cost of equity understates a levered firm. Both errors are detectable by asking one question of a spreadsheet: does this flow already have interest taken out, and does this rate already have leverage priced in?

**Interest coverage** is the credit-side analogue, and it comes in a family:

$$
\frac{\mathrm{EBIT}}{\mathrm{Int}}, \qquad \frac{\mathrm{EBITDA}}{\mathrm{Int}}, \qquad \frac{\mathrm{EBITDA} - \mathrm{Capex}}{\mathrm{Int}}.
$$

$$\mathrm{EBITDA}$$ — earnings before interest, taxes, depreciation and amortization — is not a GAAP measure and has no fixed definition. In a credit agreement it means whatever the definitions section says, and that section carries a negotiated list of permitted add-backs; §24.1's covenant arithmetic runs on ratios of exactly this kind, and its data exercise asks the reader to find the add-backs and price the slack. The third variant exists because the first two treat capital expenditure as free, which for a capital-intensive borrower it conspicuously is not.

***

## C.3 How the Three Statements Articulate

### C.3.1 The three linking identities

![Figure C.1: How the three statements articulate](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-5ff12916cae4942b4fe2bd791730533b815c85bc%2Ffig_C_01_articulation.png?alt=media)

**Figure C.1: How the three statements articulate.** The three statements are not three reports; they are three views of one set of transactions, joined by identities that hold exactly. Net income closes into retained earnings on the balance sheet, and it also opens the cash flow statement, which is why the same number appears twice in every annual report. The three sections of the cash flow statement then sum to the change in the cash line of the balance sheet. Read the diagram as a set of constraints rather than as a workflow: any two of the three statements determine the third, which is what makes an inconsistency between them a detectable error rather than a matter of opinion. The one gap in the picture is the one that matters for this book. The retained-earnings identity holds exactly only under clean surplus, and real accounting is not clean-surplus — other comprehensive income bypasses the income statement and accumulates directly in equity. That exception is the mechanism by which a bank's securities losses can sit inside its book equity and outside its reported earnings at the same time, which is §C.4.2 and the accounting behind the 2023 failures. *Source: Author's construction from Section C.3.1.*

The statements are not three independent reports. They are three views of one set of transactions, joined by identities that hold exactly.

**Retained earnings roll forward with net income and dividends:**

$$
\mathrm{RE}\_t = \mathrm{RE} \_{t-1} + \mathrm{NI}\_t - \mathrm{Div}\_t.
$$

**Cash rolls forward with the three sections of the cash flow statement:**

$$
\mathrm{Cash}\_t = \mathrm{Cash} \_{t-1} + \mathrm{CFO}\_t + \mathrm{CFI}\_t + \mathrm{CFF}\_t.
$$

**Operating cash flow is net income with the accruals undone:**

$$
\mathrm{CFO}\_t = \mathrm{NI}\_t + \text{non-cash charges} - \Delta(\text{non-cash working capital}).
$$

The first identity is exact only under **clean surplus**, the condition that all changes in equity other than transactions with owners pass through net income. Real accounting is not clean-surplus: other comprehensive income — unrealized gains on available-for-sale securities, pension remeasurements, currency translation — bypasses the income statement and accumulates directly in equity, so the exact statement adds $$\mathrm{OCI}\_t$$ and subtracts repurchases and issuance. That exception is the mechanism by which a bank's securities losses sit inside its book equity and outside its reported earnings at once, which is §C.4.2.

### C.3.2 One firm-year, built from transactions

Meridian Tool Works is a fictional manufacturer. Its opening balance sheet is the first column of Table C.5, both sides totalling 1,280. The year runs as follows.

**Table C.3: The year's transactions ($ millions)**

| #  | Transaction                                       | Amount |
| -- | ------------------------------------------------- | ------ |
| 1  | Sales, all on credit                              | 1,000  |
| 2  | Cost of the goods sold, released from inventory   | 600    |
| 3  | Inventory purchased on account                    | 640    |
| 4  | Cash collected from customers                     | 950    |
| 5  | Cash paid to suppliers                            | 610    |
| 6  | Selling and administrative expenses, paid in cash | 170    |
| 7  | Depreciation of property, plant and equipment     | 100    |
| 8  | Capital expenditure, paid in cash                 | 120    |
| 9  | Interest paid on long-term debt                   | 30     |
| 10 | Income tax at 21 percent, paid in cash            | 21     |
| 11 | Long-term debt issued 100, repaid 40 (net)        | 60     |
| 12 | Dividends paid 30; shares repurchased 20          | 50     |

*Source: Author's construction*

**Table C.4: The income statement and the cash flow statement ($ millions)**

| Income statement           |         | Cash flow statement      |           |
| -------------------------- | ------- | ------------------------ | --------- |
| Revenue                    | 1,000   | Net income               | 79        |
| Cost of goods sold         | (600)   | Depreciation             | 100       |
| Selling and administrative | (170)   | Increase in receivables  | (50)      |
| Depreciation               | (100)   | Increase in inventory    | (40)      |
| **EBIT**                   | **130** | Increase in payables     | 30        |
| Interest expense           | (30)    | **Cash from operations** | **119**   |
| **Pre-tax income**         | **100** | Capital expenditure      | (120)     |
| Income tax at 21%          | (21)    | **Cash from investing**  | **(120)** |
| **Net income**             | **79**  | Net borrowing            | 60        |
|                            |         | Dividends paid           | (30)      |
| Memo: EBITDA               | 230     | Shares repurchased       | (20)      |
|                            |         | **Cash from financing**  | **10**    |
|                            |         | **Change in cash**       | **9**     |

*Source: Author's construction*

**Table C.5: The balance sheet, opening and closing ($ millions)**

|                                   | Opening   | Closing   |                                  | Opening   | Closing   |
| --------------------------------- | --------- | --------- | -------------------------------- | --------- | --------- |
| Cash                              | 120       | 129       | Accounts payable                 | 150       | 180       |
| Accounts receivable               | 200       | 250       | Long-term debt                   | 500       | 560       |
| Inventory                         | 260       | 300       | **Total liabilities**            | **650**   | **740**   |
| Net property, plant and equipment | 700       | 720       | Paid-in capital                  | 300       | 300       |
|                                   |           |           | Treasury stock                   | 0         | (20)      |
|                                   |           |           | Retained earnings                | 330       | 379       |
|                                   |           |           | **Total equity**                 | **630**   | **659**   |
| **Total assets**                  | **1,280** | **1,399** | **Total liabilities and equity** | **1,280** | **1,399** |

*Source: Author's construction*

Now verify the articulation, which is the exercise. Retained earnings: 330 plus 79 less 30 is 379. Cash: 120 plus 119 less 120 plus 10 is 129. Property, plant and equipment: 700 plus 120 less 100 is 720. Operating cash flow the long way round: collections 950, less 610 to suppliers, less 170 of cash operating expenses, less interest 30, less tax 21, gives 119 — the number the indirect method reached by starting at net income and undoing four accruals. And both sides of the closing balance sheet total 1,399.

Notice what the year looked like from each statement. The income statement reports a profitable year, 79 on sales of 1,000. The cash flow statement reports a business that generated 119 of cash, spent 120 on plant, and paid 50 to shareholders financed by 60 of new borrowing. The balance sheet reports growth: assets up 119, funded by 90 of new liabilities and 29 of retained equity. Three true accounts of one year. Chapter 25's claim that firms finance themselves internally is visible in one line — 119 of operating cash against 120 of capital expenditure — and the 60 of net borrowing went to shareholders, not to the plant.

### C.3.3 Accruals, and what cash does not tell you

**Total accruals** are the wedge between the two profit measures, scaled so firms of different sizes are comparable:

$$
\mathrm{ACC}\_t = \frac{\mathrm{NI}\_t - \mathrm{CFO}\_t}{\bar{A}\_t},
$$

with $$\bar{A}\_t$$ average total assets over the year. For Meridian this is −40 over 1,339.5, or −0.030. Accruals are negative, meaning cash exceeded reported profit, because depreciation of 100 exceeded the 60 of working-capital investment set against it.

Sloan (1996) made this a variable rather than a footnote: firms with high accruals — reported earnings well in excess of cash — subsequently underperform, and firms with low accruals outperform, by enough to sustain a strategy. The accounting interpretation is that the accrual component of earnings is less persistent than the cash component, because accruals embed estimates that reverse, and that investors price the two as though equally durable. The behavioral interpretation is the same sentence with "fail to distinguish" for "price as though." This lands in Chapter 6's factor zoo as the cleanest case of a return predictor whose construction is entirely an accounting choice.

Two measurement warnings change the answer. Accruals were originally computed from successive balance sheets — the change in non-cash working capital less depreciation — and Hribar and Collins (2002) showed this introduces error whenever the balance sheet moves for a reason other than operations, chiefly acquisitions and divestitures, which are precisely the firms most likely to sit in the extreme deciles; the cash-flow-statement measure above avoids it. And accruals are mechanically related to growth, so an accruals sort is partly an investment sort, which is why the accrual and investment factors are correlated (Ch 6 §6.2). Dechow, Ge and Schrand (2010) survey the earnings-quality literature this opened.

Table C.6 collects the quantities the body chapters use, computed on Meridian, with market equity assumed to be 1,318 — fifty million shares at $26.36.

**Table C.6: The ratios this book computes, on one firm-year**

| Quantity                        | Definition                                                                                               | Meridian | Used in                                    |
| ------------------------------- | -------------------------------------------------------------------------------------------------------- | -------- | ------------------------------------------ |
| Book equity $$\mathrm{BE}$$     | Assets less liabilities; for the standard sorts, stockholders' equity plus deferred taxes less preferred | 659      | Chs 6, 22, 23                              |
| Market equity $$\mathrm{ME}$$   | Price times shares outstanding                                                                           | 1,318    | Chs 6, 20, 22                              |
| Market-to-book                  | $$\mathrm{ME}/\mathrm{BE}$$                                                                              | 2.00     | Ch 22 §22.2; reciprocal is Ch 6's HML sort |
| Book leverage (assets)          | $$\mathrm{BD}/A$$                                                                                        | 0.40     | Ch 23 §23.6                                |
| Book leverage (capital)         | $$\mathrm{BD}/(\mathrm{BD}+\mathrm{BE})$$                                                                | 0.46     | Ch 23 §23.2                                |
| Market leverage                 | $$\mathrm{BD}/(\mathrm{BD}+\mathrm{ME})$$                                                                | 0.30     | Ch 23 §23.6                                |
| Balance-sheet leverage $$L$$    | $$A/E$$                                                                                                  | 2.12     | Ch 16 §16.1                                |
| Net debt to EBITDA              | $$(\mathrm{BD}-\mathrm{Cash})/\mathrm{EBITDA}$$                                                          | 1.87     | Ch 24 §24.1                                |
| Interest coverage               | $$\mathrm{EBIT}/\mathrm{Int}$$                                                                           | 4.33     | Ch 24 §24.1                                |
| Interest coverage (EBITDA)      | $$\mathrm{EBITDA}/\mathrm{Int}$$                                                                         | 7.67     | Ch 24 §24.1                                |
| Payout ratio $$\mathrm{POR}$$   | $$\mathrm{Div}/\mathrm{NI}$$                                                                             | 0.38     | Ch 23 §23.5                                |
| Total payout ratio              | $$(\mathrm{Div}+\text{repurchases})/\mathrm{NI}$$                                                        | 0.63     | Ch 23 §23.5                                |
| $$\mathrm{FCFF}$$               | $$\mathrm{EBIT}(1-\tau\_c)+\mathrm{Dep}-\Delta\mathrm{NWC}-\mathrm{Capex}$$                              | 22.7     | Ch 22 §22.2                                |
| $$\mathrm{FCFE}$$               | $$\mathrm{FCFF}-\mathrm{Int}(1-\tau\_c)+\Delta\mathrm{BD}$$                                              | 59.0     | Ch 22 §22.2                                |
| $$\mathrm{CFO}-\mathrm{Capex}$$ | The press's "free cash flow"                                                                             | −1.0     | §C.2.4                                     |
| Accruals $$\mathrm{ACC}$$       | $$(\mathrm{NI}-\mathrm{CFO})/\bar{A}$$                                                                   | −0.030   | Ch 6 §6.2, §C.3.3                          |
| Tobin's $$\mathrm{Q}$$, crude   | $$(\mathrm{ME}+\mathrm{BD})/A$$, book assets standing in for replacement cost                            | 1.34     | Ch 22 §22.4                                |

*Source: Author's calculation from Tables C.3-C.5, with market equity of 1,318 assumed*

The last row carries the caveat §22.4 makes at length: book assets are not replacement cost, and for an intangible-intensive firm they are not close, so a crude Q is an upper bound on the ratio the theory wants.

***

## C.4 Financial Firms Are Different

Everything above describes a firm that makes things. Most of the balance sheets in this book belong to firms whose product is a claim, and for them several conventions invert.

### C.4.1 Why a bank's balance sheet reads inverted

A bank's assets are loans and securities — promises other people have made to it. Its liabilities are deposits and borrowings — promises it has made to other people. The deposit that is an asset in Chapter 2's household table is a liability here: Chapter 2's pairing observation in its most familiar instance.

**Table C.7: A stylized bank balance sheet ($ billions)**

| Assets                                               | Carrying value | Liabilities and equity              | Carrying value |
| ---------------------------------------------------- | -------------- | ----------------------------------- | -------------- |
| Cash and reserves                                    | 8.0            | Deposits                            | 80.0           |
| Securities, available for sale (amortized cost 12.0) | 10.5           | Long-term debt and other borrowings | 8.0            |
| Securities, held to maturity (fair value 17.0)       | 20.0           | Other liabilities                   | 3.0            |
| Loans, net of allowance                              | 55.0           | **Total liabilities**               | **91.0**       |
| Goodwill and other intangibles                       | 1.5            | Preferred stock                     | 1.0            |
| Other assets                                         | 5.0            | Common equity                       | 8.0            |
| **Total assets**                                     | **100.0**      | **Total liabilities and equity**    | **100.0**      |

*Source: Author's construction*

Leverage in §16.1's sense is $$L = A/E$$, here 100 over 9, or 11.1 — unremarkable for a commercial bank and alarming for a manufacturer. The reason is the liability side: deposits are the cheapest and stickiest funding in the economy, and a bank's franchise is substantially the spread between what it earns on assets and what it pays for them (Drechsler, Savov and Schnabl 2021). The income statement inverts too. There is no revenue line in the ordinary sense; there is **net interest income** — interest earned less interest paid — plus fee income, less the **provision for credit losses**, less operating expense. The provision is an accrual of the kind §C.2.2 described, and since 2020 large US banks have set it under the current expected credit loss standard, which requires a lifetime loss estimate at origination rather than a loss recognized when incurred — moving provisioning earlier in the cycle and making bank earnings a function of macroeconomic forecasts.

### C.4.2 Banking book against trading book

The most consequential accounting distinction in this book is between securities a bank intends to hold and securities it intends to trade.

**Held to maturity** securities are carried at **amortized cost**. If the bank asserts both the intent and the ability to hold to maturity, changes in market value appear neither on the balance sheet nor in income. They are disclosed in a footnote and in Call Report Schedule RC-B, and nowhere else. In Table C.7 that book has an amortized cost of 20.0 and a fair value of 17.0: a 3.0 unrealized loss, disclosed and invisible.

**Available for sale** securities are carried at **fair value**, with unrealized gains and losses running through other comprehensive income rather than earnings. The available-for-sale book above shows 10.5 against an amortized cost of 12.0, so a 1.5 loss is already inside reported common equity of 8.0.

**Trading** securities are carried at fair value with changes running through net income immediately.

Now the arithmetic that made 2023. Reported equity is 9.0 and the loss kept out of it is 3.0, a third of the total. Nothing forces recognition — until the bank has to sell, at which point the loss is realized in earnings and, under the tainting rules, a sale from the held-to-maturity portfolio can force reclassification of the rest to fair value. A deposit outflow converts a footnote into an insolvency. That is the sense in which a rise in interest rates is a solvency event for a bank and not merely a mark, which is §19.3's claim; Jiang, Matvos, Piskorski and Seru (2024) put the US banking system's mark-to-market losses at roughly two trillion dollars in early 2023 and showed how the exposure interacted with the uninsured-deposit share. The accounting convention was a necessary condition for Silicon Valley Bank's failure: the losses were public, in the footnotes, for anyone who read them.

### C.4.3 Regulatory capital against book equity

§16.1's leverage algebra needs a stated definition of $$E$$, because a bank has at least five and they differ by nearly a factor of two.

**Table C.8: Five definitions of the Table C.7 bank's equity ($ billions)**

| Definition                  | Construction                                                                | Value                             |
| --------------------------- | --------------------------------------------------------------------------- | --------------------------------- |
| Total book equity           | Assets less liabilities, GAAP                                               | 9.0                               |
| Common equity               | Less preferred stock                                                        | 8.0                               |
| Tangible common equity      | Less goodwill and other intangibles                                         | 6.5                               |
| Common equity tier 1 (CET1) | Tangible common equity, adjusted for accumulated other comprehensive income | 6.5, or 8.0 with the AOCI opt-out |
| Mark-to-market equity       | Common equity less the held-to-maturity unrealized loss                     | 5.0                               |

*Source: Author's construction. Regulatory adjustments are simplified; deferred tax assets and mortgage-servicing rights carry their own deductions and thresholds.*

The regulatory ratios divide one of these by one of several denominators. Against **risk-weighted assets** of, say, 55 — the schedule assigns zero to reserves and Treasuries, low weights to agency securities and residential mortgages, and one hundred percent to most corporate credit — CET1 over risk-weighted assets is 11.8 percent, or 14.5 percent for a bank that has elected out of including accumulated other comprehensive income. Against **average total assets** of 100 the tier 1 leverage ratio is 7.5 percent. Against a **supplementary leverage ratio exposure measure** of 120, which adds off-balance-sheet commitments and derivative exposures, it is 6.25 percent. Same bank, same day, capital ratios from 6.25 to 14.5 percent.

Three points follow. The **risk weights** are why a bank's demand for a claim depends on its regulatory treatment and not only its expected return — the same structure as the insurers' schedule in §C.4.4, and the mechanism of §19.3. The **non-risk-weighted** ratios are why Chapter 19's supplementary leverage ratio charges the same capital against a Treasury as against a leveraged loan, and why the April 2020 exclusion of Treasuries and reserves from that denominator was an admission about balance-sheet scarcity. And the **AOCI opt-out**, available to banks outside the largest category, is why an unrealized loss can sit inside book equity and outside regulatory capital at once. When §16.1 writes $$L = A/E$$ it means Table C.8's first row unless it says otherwise, and any bank leverage series must say which row it used.

### C.4.4 Insurance accounting

An insurer keeps two sets of books, and neither is optional. **GAAP** statements, filed with the SEC by publicly traded insurers, follow §§C.1-C.3 with insurance-specific modifications, including a deferred acquisition cost asset spreading the cost of writing a policy over its life. **Statutory accounting** (SAP), filed with the state of domicile on the NAIC's annual statement blank, answers a different question: could this insurer pay its claims if it stopped writing business today? Its conservatism is systematic. **Non-admitted assets** — furniture, most equipment, overdue receivables, certain deferred tax assets — are excluded from the balance sheet entirely, as unavailable to pay claims. Acquisition costs are expensed as incurred rather than deferred, so a fast-growing life insurer reports worse statutory than GAAP results, an effect called new-business strain. The residual is **policyholders' surplus** rather than equity, and it is the number the regulator watches.

**Policy reserves** are the largest liability and the one least like corporate debt. A reserve is not a promise to pay a stated amount on a stated date; it is an actuarial estimate of the present value of claims on contracts already written, computed under prescribed mortality and morbidity tables and a prescribed maximum valuation interest rate. Two consequences matter for §16.2. The liability does not move with market rates the way an economically equivalent bond would, because the discount rate is prescribed rather than observed; and most of the bond portfolio backing it is also carried at amortized cost, for insurers holding NAIC designation 1 and 2 paper. Statutory accounting is thus largely historical cost on both sides, which is why the constrained behavior Koijen and Yogo (2015) document takes the form of selling *policies* below actuarial value rather than selling bonds.

**Risk-based capital** converts the portfolio into a required-capital number. The formula assigns charges to asset, insurance, interest-rate and business risk, then combines them with a square-root covariance adjustment crediting diversification across categories, producing Authorized Control Level RBC. The published ratio is total adjusted capital over that number, and the regulatory ladder begins at 200 percent, with more intrusive intervention at 150, 100 and 70. Chapter 16's Table 16.3 reports the asset-risk factors; the feature driving the economics is that they are nearly flat across the investment-grade buckets, which is the incentive to hold the highest-yielding bond inside a bucket that Becker and Ivashina (2015) document.

### C.4.5 Investment company accounting

A mutual fund or ETF has the simplest balance sheet in finance and the most tightly regulated valuation process. Net asset value per share is

$$
\mathrm{NAV} = \frac{\text{assets} - \text{liabilities}}{\text{shares outstanding}},
$$

computed once each business day. Three features of that computation carry economic content.

**The daily strike.** Under the forward-pricing rule, an order received before the fund's cutoff — normally 4:00 pm Eastern — is executed at the net asset value computed *after* the close. Nobody transacts at a known price. The 2003 market-timing and late-trading scandals were violations of this rule, which exists because a stale price is a free option for whoever may trade on it.

**Fair-value pricing of stale marks.** A US fund holding Japanese equities strikes a 4:00 pm New York net asset value using closing prices from a market that shut fourteen hours earlier. Unadjusted, a trader who has watched the S\&P 500 rise since then can buy the fund at yesterday's Tokyo prices. Funds therefore adjust stale prices toward a fair value estimate, under a board-supervised process the SEC formalized in 2020. The same problem where nothing traded at all produced §17.5's March 2020 episode: bond ETFs at discounts of several percent to net asset value, and which number was wrong is a question about whether the NAV's inputs were prices or quotes.

**In-kind redemption.** When an authorized participant redeems a creation unit the fund delivers securities rather than cash, and a regulated investment company recognizes no taxable gain on that distribution. The fund hands out its lowest-basis lots, and the embedded gain leaves without ever being realized inside the fund. That provision, not portfolio turnover, is the accounting basis for the ETF's tax advantage over the mutual fund — a wrapper effect, as §17.2 puts it, and worth nothing inside a tax-deferred account.

### C.4.6 Private fund accounting

A private fund's assets have no prices, so its accounts report fair values estimated under the fund's own valuation policy, which lives in the limited partnership agreement. The framework is §C.1.3's ASC 820 hierarchy, and essentially every position is Level 3: a model with unobservable inputs, typically a multiple applied to a portfolio company's trailing earnings, cross-checked against a discounted cash flow and the last round's price. The general partner prepares the mark, a valuation committee approves it, and the auditor tests whether it is reasonable. None of those steps is a transaction, and none produces a price in the sense Chapter 3 uses the word.

The consequence for Chapter 18 is direct. The residual value in a multiple, the terminal cash flow in an internal rate of return, and the numerator of the public market equivalent all use a reported net asset value that is a model output produced by the party whose performance is being measured. Kaplan and Schoar's (2005) public market equivalent is the least contaminated because it weights realized cash flows, but it still carries the final NAV. §18.2's smoothing arithmetic — reported returns that are a weighted average of true returns, and therefore an understated beta — is an econometric consequence of an accounting policy written by the general partner.

***

## C.5 Reading a Filing

### C.5.1 The 10-K, and the four places the information is

A US-listed company's annual report on Form 10-K runs to a few hundred pages in four parts, and a reader who knows where to look can extract what this book needs in twenty minutes.

**Part I** describes the business (Item 1) and the risk factors (Item 1A). Item 1A is written by lawyers to be unfalsifiable — but it is boilerplate that changes, and the year-over-year diff is informative.

**Part II** holds the useful material. Item 5 includes the monthly table of **issuer purchases of equity securities**, which is §23.5's repurchase data at monthly frequency with the remaining authorization. Item 7 is management's discussion and analysis, where the firm explains its own numbers and reconciles non-GAAP measures to GAAP ones. Item 7A is the market-risk disclosure and, for a bank, the source of the trading value-at-risk figures Chapter 26's data exercise uses. Item 8 is the financial statements and, crucially, the notes.

**Part III** — directors, compensation, beneficial ownership — is almost always incorporated by reference from the proxy statement, Form DEF 14A, a separate filing and the source for Chapter 24's governance exercises.

**Part IV**, Item 15, is the exhibit index: least read and often most valuable, because credit agreements, indentures and material contracts are filed as exhibits. §24.1's covenants live in an exhibit, with the definitions section that fixes EBITDA and its add-backs.

All of it is free on EDGAR, which supports full-text search and exposes structured XBRL data through the company-facts and frames APIs at data.sec.gov, so a panel of any tagged line item can be assembled without a data licence. Appendix B §B.6 lists the filing types this book uses.

### C.5.2 The four footnotes that matter here

**The fair value hierarchy note** tabulates assets and liabilities measured at fair value by Level 1, 2 and 3, with a roll-forward of the Level 3 balance. The share of assets in Level 3, and the traffic in and out of it, is the closest thing to a disclosure of how much of the balance sheet is an opinion.

**The pension note** reports the projected benefit obligation, the fair value of plan assets, the funded status that lands on the balance sheet, and the assumptions: discount rate, expected long-run return on plan assets, mortality table. The discount rate is a high-grade corporate bond yield, so the obligation moves with credit spreads; the expected return is a choice; and the plan's asset allocation makes the sponsor a leveraged investor in whatever it holds. §16.2's defined-benefit story is visible here one sponsor at a time.

**The debt note** carries the maturity schedule — amounts due in each of the next five years and thereafter — the coupon and maturity of each issue, a description of covenants, and the fair value of total debt against its carrying value, which is where §C.1.3's liability-side divergence is quantified. It is the raw material for a refinancing-risk assessment and for Table C.6's market-leverage ratio.

**The share repurchase disclosure** is technically Part II Item 5 rather than a note, but it belongs here. Monthly counts, average prices paid and the remaining authorization distinguish a firm executing an announced program from one that announced and stopped — a distinction §23.5 needs and the cash flow statement's single annual line cannot supply.

### C.5.3 Two filings that are not 10-Ks

**A bank holding company's Call Report.** Every insured US depository files quarterly with the FFIEC, free from the Central Data Repository, with the derived Uniform Bank Performance Report alongside. The schedules to read, in order: **RC**, the balance sheet, which is Table C.7 in the real format; **RC-B**, securities, reporting amortized cost *and* fair value in separate columns for held-to-maturity and available-for-sale portfolios, where §C.4.2's unrealized loss is found and where it sat throughout 2022; **RC-C**, loans by category; **RC-E**, deposits, including the estimated uninsured portion, the other half of the 2023 fragility calculation; **RC-R**, regulatory capital, which walks from total equity to CET1 and reports risk-weighted assets, so Table C.8's five definitions can be built for a real institution; and **RI**, the income statement, separating net interest income, the provision and fee income. The exercise behind §19.3's claim: pick a bank that failed in 2023 and one that did not, pull RC-B and RC-E for 2021 and 2022, and compute each quarter's ratio of the held-to-maturity unrealized loss to total equity, and the share of deposits above the insurance limit. Both numbers were public before either bank failed.

**An insurer's statutory annual statement.** The NAIC annual statement blank has a fixed page structure: the Assets page, showing admitted assets only; the Liabilities, Surplus and Other Funds page, where policy reserves dominate and the residual is surplus; the Summary of Operations, which is the statutory income statement; the Five-Year Historical Data exhibit; and **Schedule D**, listing every bond the insurer owns, CUSIP by CUSIP, with book-adjusted carrying value, fair value and NAIC designation. Schedule D is why the reach-for-yield literature exists: a position-level portfolio disclosure of a kind no other institutional sector provides. The NAIC's consolidated database is licensed, but individual statements are posted free by a number of state insurance departments, and public insurers' EDGAR filings carry statutory summaries in the notes.

The habit to build from both filings is the one this appendix has been arguing for throughout. Every line in either document is a claim, held by somebody the book has a chapter about, and the convention governing how that line is measured is not a technicality standing between the reader and the economics. It is frequently the economics.

***

*Further depth: Penman (2013) for statement analysis oriented toward valuation, with Nissim and Penman (2001) as the compact version of its ratio apparatus; for financial institutions, the FFIEC's Call Report instructions and the NAIC's Accounting Practices and Procedures Manual.*