> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-v-firms-as-issuers-of-claims/chapter_23_capital_structure.md).

# Chapter 23: Capital Structure and Payout

*Part V: Firms as Issuers of Claims — Financial Economics: Claims, Prices, and Holders*

***

## Opening Episode: The Richest Company in the World Borrows Seventeen Billion Dollars

On 30 April 2013, Apple sold seventeen billion dollars of bonds in six tranches. It was, at the time, the largest corporate bond offering on record, exceeding the previous mark set by a pharmaceutical issuer four years earlier. The order book was reported in the press to have run to several times the deal size, and the ten-year tranche priced at a spread of well under a hundred basis points over Treasuries.

The company had not borrowed in the public bond market since the 1990s. It did not need the money. Its fiscal second-quarter filing, for the period ended in late March 2013, reported cash, cash equivalents and marketable securities of roughly one hundred and forty-five billion dollars — more than the market capitalization of most companies in the index it belonged to. A firm sitting on a hundred and forty-five billion dollars of cash went out and borrowed seventeen billion more.

The proceeds did not fund a factory. A week earlier, on 23 April, Apple had announced an expansion of its capital return program to about one hundred billion dollars through the end of calendar 2015, roughly doubling the prior commitment. The share repurchase authorization went from ten billion dollars to sixty; the quarterly dividend, reinstated only the year before, was raised by about fifteen percent. The bond deal financed a payout.

Three forces produced that arrangement, and each is a section of this chapter.

**Taxes explain the simultaneous cash and debt.** The great majority of Apple's cash — well over two thirds, on the company's own disclosures and contemporaneous analyst estimates — was held by foreign subsidiaries. Under the international tax rules then in force, repatriating those earnings would have triggered US corporate tax at a thirty-five percent statutory rate, net of foreign tax credits. Domestic cash was a different and much smaller pool. Borrowing at a coupon near two percent against foreign cash earning very little was cheaper than paying a repatriation toll of thirty-odd cents on the dollar, and the interest was deductible besides. Holding a large gross cash position and a large gross debt position at the same time is irrational under any theory in which only *net* debt matters. It is entirely rational once a tax wedge sits between the two sides of the balance sheet.

**Payout, not investment, was the decision variable.** The question in the room was not which projects to fund. It was how much cash to return, in what form, and how to finance the return. That is the question §23.5 takes up, and it is why this chapter merges two topics that older textbooks separate: the financing decision and the payout decision are the same decision seen from two ends of the balance sheet.

**Holders drove it.** In February 2013 David Einhorn's Greenlight Capital had proposed that Apple distribute perpetual preferred stock — "iPrefs" — to its shareholders, and had gone to court to block a proxy proposal that would have removed the board's authority to issue blank-check preferred without a shareholder vote; the court ruled for Greenlight and Apple withdrew the item. By August, Carl Icahn had disclosed a stake and was publicly pressing for a far larger buyback. The capital structure that emerged was not chosen in a vacuum by managers optimizing a textbook objective. It was negotiated with the people who held the claims.

And then the last turn, which §23.7 returns to. Seventeen billion dollars of highly rated corporate paper found buyers instantly, at a spread that was small by any historical standard, at a moment when the safe-asset shortage of Chapter 9 §9.4 and the reaching-for-yield behavior of Chapter 10 §10.9 were both well documented. Apple did not merely finance a payout. It manufactured, on demand, exactly the claim that the largest holders in the market were straining to buy.

Modigliani and Miller's theorem says none of this should matter. Understanding precisely which of their assumptions each of the three forces violates is the whole of what follows.

***

## 23.1 Modigliani-Miller: The Proposition and Its Assumptions

### The proposition

Chapter 21 §21.4 established that a security is an allocation of cash-flow and control rights across states of the world, and its Table 21.3 laid out the standard menu. Capital structure is the question of how to slice that bundle. **Modigliani and Miller's irrelevance proposition** answers: in a frictionless market, the slicing does not change the size of what is sliced.

> **Proposition I.** The market value of a firm is independent of its capital structure: $$V\_L = V\_U$$, where $$V\_U$$ is the value of an all-equity firm and $$V\_L$$ the value of an otherwise identical levered firm.

The proof is Chapter 3's, and it is worth doing the Chapter 3 way rather than quoting the conclusion, because the *method* is what generalizes. Chapter 3 §3.2 established that prices are linear: if two portfolios deliver the same payoff in every state, they have the same price, and the price of a sum is the sum of the prices. Debt and equity are a partition of the firm's payoff. Buy all of a levered firm's debt and all of its equity, and you own the whole payoff — the same payoff an all-equity firm delivers. By linearity, the two must cost the same.

### Homemade leverage, in numbers

The replication argument is what makes the linearity concrete, and it is the argument Modigliani and Miller actually ran. Consider two firms with identical assets producing a perpetual expected operating cash flow of one thousand per year. Firm U is all equity and worth ten thousand, so its assets earn $$r\_U = 10$$ percent. Firm L has four thousand of riskless perpetual debt at $$r\_D = 5$$ percent, paying two hundred of interest and leaving eight hundred for its equity.

If Proposition I holds, L's equity is worth $$10{,}000 - 4{,}000 = 6{,}000$$, and its expected return is $$800/6{,}000 = 13.33$$ percent. That is **Proposition II**, the statement that leverage raises the cost of equity exactly enough to leave the weighted average unchanged:

$$
r\_E = r\_U + \frac{D}{E}(r\_U - r\_D) = 0.10 + \frac{4{,}000}{6{,}000}(0.10-0.05) = 13.33\text{ percent},
$$

and the weighted average cost of capital is $$0.6\times 13.33 + 0.4\times 5 = 10$$ percent, which is $$r\_U$$. Leverage rearranges risk between the two claims; it does not create or destroy any. Figure 23.1 is both propositions at once.

![Figure 23.1: Modigliani-Miller](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-9803eabf6a444d3ced9ac2537e9b80f74c07063b%2Ffig_23_01_modigliani_miller.png?alt=media)

**Figure 23.1: Modigliani-Miller.** The chapter's two firms, with leverage allowed to vary. Panel (a): the value of the firm is flat at 10,000 at every debt ratio, and the two shaded regions are the partition of that value between the claims. The whole content of Proposition I is that the top line does not move; the marker is firm L, with 4,000 of debt and 6,000 of equity. Panel (b): what each claim then has to earn. The cost of equity rises linearly in D/E with slope r\_U − r\_D, from 10 percent at no leverage to 13.33 percent at firm L's ratio, and the weighted average stays at r\_U throughout. Debt is riskless here, as it is in the chapter's arithmetic, which is why r\_D is drawn flat; once debt is risky its own required return rises, the cost of equity flattens correspondingly, and the weighted average is still flat. Nothing on either panel is measured, and nothing needs to be: the proposition is an arbitrage result, and the figure is what it looks like. *Source: Author's construction from the worked firms of §23.1.*

Now suppose an investor wants L's thirteen-and-a-third percent expected return but only U's shares exist. She puts up six thousand of her own money, borrows four thousand at five percent, and buys ten thousand of U. Her payoff is $$1{,}000 - 200 = 800$$ on six thousand invested: exactly L's equity return, manufactured at home. **Homemade leverage** is the mechanism, and it runs in both directions — an investor holding one percent of L's equity *and* one percent of L's debt has paid one hundred for a payoff of ten, which is one percent of U.

The arbitrage bites if the market prices the two differently. Suppose L's equity trades at 6,500, so $$V\_L = 10{,}500$$. Sell short one percent of L's equity for 65; borrow one percent of L's debt, 40; buy one percent of U for 100. Cash today: $$65 + 40 - 100 = +5$$. Every year thereafter you receive ten from U, pay eight to the equity you shorted, and pay two of interest — a net flow of exactly zero, forever. Five today for nothing later, and the trade scales: at full size it is five hundred, and it closes only when $$V\_L$$ falls back to $$V\_U$$. That is the proof. Not an equilibrium condition on preferences, and no assumption about what anyone wants — just a portfolio that costs less than an identical portfolio.

### What the proof assumes is the chapter's map

The irrelevance result is not a description of the world and was never offered as one. It is a device for locating the frictions that matter, in the way a frictionless plane locates friction. Every assumption the replication argument leans on is a candidate explanation for capital structure, and each becomes a section of this chapter or a pointer out of it.

**Table 23.1: What Modigliani-Miller assumes, and where each failure leads**

| The proof requires                                                    | Failing it means                                                                                     | Treated in         |
| --------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------- | ------------------ |
| No taxes distinguishing debt from equity payments                     | Interest is deductible and personal tax rates differ by claim                                        | §23.2              |
| No costs of default beyond the transfer of assets                     | Bankruptcy consumes resources and distorts decisions before it arrives                               | §23.2              |
| Managers and investors know the same things                           | Issuing a claim reveals what management believes it is worth                                         | §23.3              |
| Prices are correct, so timing is impossible                           | Managers can believe their claims are mispriced and act on it                                        | §23.4              |
| Investment is fixed and independent of financing                      | Financing changes what managers do — free cash flow, risk-shifting, debt overhang                    | §§23.5-23.6, Ch 24 |
| Investors can replicate any capital structure at the firm's own terms | Holders are segmented, mandated, and capital-constrained, so who *can* hold a claim differs by claim | §23.7              |

*Source: Author's construction, following the assumption list in Modigliani and Miller (1958). The rows are stated as the replication argument uses them, not as the original paper enumerates them.*

Read the table as a single sentence, which is the one to carry out of this section: **capital structure is a way of slicing Chapter 21 §21.4's bundle of cash-flow and control rights, and slicing changes nothing unless a slice changes taxes, incentives, information, or who is able to hold it.** The first three of those are the standard corporate finance syllabus. The fourth is this book's, and it is the last row of the table.

The table is a research agenda and not a museum, and the clearest sign of that is that securities get designed against particular rows of it. Contingent capital — a claim that is debt while the firm is sound and converts to equity on a trigger — is engineered directly against row two, buying the deduction and the discipline of debt while removing the distress state the deduction is paid for; Bolton and Samama's capital-access design is one version, and the instrument is now a standard layer in the bank capital stack of Chapter 19 §19.2. A row of an assumption list, read by someone with an underwriter, is a product specification.

One qualification on the last row before the machinery starts. Homemade leverage assumes the investor borrows on the firm's terms. Real investors face margin rules, leverage constraints, and mandates — the same constraints Chapter 4 §4.9's betting-against-beta argument prices, and Chapter 16 §16.2's regulatory capital schedules impose. A pension plan forbidden to use leverage cannot manufacture levered equity at home and will pay a premium for a firm that manufactures it instead. The replication that proves irrelevance is precisely the operation Part IV spent seven chapters showing that holders cannot always perform.

***

## 23.2 The Trade-off Theory

### The tax shield

Interest is deductible from corporate taxable income; dividends and repurchases are not. That is a subsidy to debt, and Modigliani and Miller's 1963 correction values it.

Take the firm above, with four thousand of permanent debt at five percent and a corporate rate $$\tau\_c = 21$$ percent. The interest deduction saves $$0.21 \times 200 = 42$$ per year. If the debt is permanent and the saving is as safe as the interest payment that generates it, discount at $$r\_D$$:

$$
\text{PV(tax shield)} = \frac{\tau\_c r\_D D}{r\_D} = \tau\_c D = 0.21 \times 4{,}000 = 840,
$$

so $$V\_L = V\_U + \tau\_c D = 10{,}840$$. The formula is memorable and the memorability is a hazard, because three things have to be true for it and none is guaranteed.

**The debt must be permanent and the discount rate must match.** A firm that maintains a target *ratio* rather than a target *level* of debt will borrow more when it is worth more, so future shields inherit the risk of the firm's assets rather than the safety of today's coupon. Discount the same forty-two per year at $$r\_U = 10$$ percent instead and the shield is worth 420 — half. The choice of discount rate is not a technicality; it is half the answer.

**The firm must have taxable income to shield.** A firm with loss carryforwards, heavy depreciation, or credits gets nothing from an additional deduction. DeAngelo and Masulis called these **non-debt tax shields** and predicted they substitute for debt. Graham's estimates of firm-specific marginal tax rates, built from simulated income paths, put many firms well below the statutory rate and imply that the typical large US firm has been leaving unused shield on the table.

**Personal taxes cut the other way.** Miller's 1977 correction is the essential one for this book, because it makes the answer depend on who holds the claim. Interest is taxed to the recipient at the rate on ordinary income, $$\theta\_d$$; equity income, which arrives partly as deferred and preferentially taxed capital gains, is taxed at an effective rate $$\theta\_e$$ that is generally lower. The net gain from a dollar of permanent debt is

$$
G\_L = \left\[1 - \frac{(1-\tau\_c)(1-\theta\_e)}{(1-\theta\_d)}\right] D .
$$

**Table 23.2: The gain from one dollar of permanent debt, under corporate and personal taxes**

| Case                                                    | $$\tau\_c$$ | $$\theta\_e$$ | $$\theta\_d$$ | Gain per dollar of debt |
| ------------------------------------------------------- | ----------- | ------------- | ------------- | ----------------------- |
| Miller's knife-edge equilibrium                         | 0.35        | 0             | 0.35          | 0.000                   |
| A high-bracket US holder, pre-2018 corporate rate       | 0.35        | 0.15          | 0.37          | +0.123                  |
| The same holder, post-2018 corporate rate               | 0.21        | 0.15          | 0.37          | −0.066                  |
| The same, with a higher effective rate on equity income | 0.21        | 0.20          | 0.37          | −0.003                  |
| **A tax-exempt marginal bondholder**                    | 0.21        | 0.15          | 0.00          | **+0.329**              |

*Source: Author's calculation from Miller (1977). Rates are illustrative combinations, not any particular year's schedule; the rate on equity income is an effective rate that already embeds deferral of capital gains.*

The first row is Miller's point: with enough debt outstanding, the marginal bondholder's tax rate rises until the corporate advantage is exactly competed away, so *aggregate* leverage is determined and no individual firm has an optimum. The last row is this book's. If the marginal buyer of corporate debt is a pension fund, an insurer's tax-favored account, or a foreign holder outside the US personal tax net, then $$\theta\_d \approx 0$$ and the gain from leverage is *larger* than $$\tau\_c$$, not smaller. The tax advantage of debt is not a property of the tax code alone. It is a property of the tax code and of the identity of the marginal holder — which is §23.7's subject, arriving early.

### Distress costs

Against the shield sits the cost of the state the shield makes more likely.

**Direct costs are small.** Legal, accounting, and advisory fees in bankruptcy have been measured repeatedly since Warner's study of railroad reorganizations, which put them at roughly one percent of the firm's market value measured years ahead of filing and around five percent at the filing itself. Later work on a broader sample of large firms finds the same order of magnitude — low single-digit percentages of assets. Direct costs alone cannot justify observed leverage restraint.

**Indirect costs are larger and harder to measure.** Customers stop buying products that need servicing or spare parts. Suppliers demand cash on delivery, tightening working capital exactly when it is scarcest. Key employees leave for firms whose equity compensation is not a lottery ticket. Managers, absorbed by creditor negotiations, defer maintenance and cut research. And the decision distortions of a levered firm arrive well before default: **debt overhang**, in which a firm declines a positive-net-present-value project because the gain accrues to creditors, and **risk-shifting**, in which equity holders with a near-worthless option prefer the high-variance strategy. Chapter 8's option view of equity, and Chapter 10 §10.2's structural model, are the pricing counterparts of both.

The best available magnitude comes from separating financial from economic distress. Andrade and Kaplan studied highly leveraged transactions that subsequently became distressed while their industries did not, and estimated the costs of *financial* distress at something on the order of ten to twenty percent of firm value. That is a large number attached to a low-probability event, which is what a trade-off theory needs.

![Figure 23.2: The trade-off](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-9e1210349f26c304b63840bb4b4cdce4937cd5a5%2Ffig_23_02_the_trade_off.png?alt=media)

**Figure 23.2: The trade-off, and whose trade-off it is.** Panel (a): the two components, per dollar of unlevered firm value. The expected cost of distress is drawn as Andrade and Kaplan's fifteen percent loss multiplied by a probability rising as the cube of leverage; the exponent is a drawing choice with no empirical content, and only the convexity matters. The three straight lines are the tax shield, taken from three rows of Table 23.2 — and they differ only in who the marginal bondholder is. Panel (b): the net of the two. A tax-exempt marginal holder puts the optimum at 86 percent debt; a high-bracket taxable holder under the pre-2018 corporate rate puts it at 52 percent; the same holder under the post-2018 rate has no interior optimum at all, because for that holder debt carries a tax penalty rather than a shield. The shaded band is roughly where US nonfinancial corporate leverage actually sits, and it is to the left of every interior optimum on the panel — which is the chapter's unused-shield puzzle, drawn. **The theory does not have one answer. It has one answer per holder, and the observed leverage of a firm is a statement about who is buying its bonds.** *Source: Author's calculation from Table 23.2 and the distress-cost estimates of §23.2.*

### The target, and the standing puzzle

Put the two together and the theory is a picture — Figure 23.2, drawn once for each of three marginal bondholders, because the shield's slope is theirs and not the firm's: value rises with leverage at rate $$\tau\_c$$, then the expected distress cost accelerates, and the optimum is where the marginal shield equals the marginal expected distress cost. Firms should have an interior **target leverage ratio**, should differ in it according to tax position and asset tangibility, and should return to it when shocks push them away.

The empirical record is partly kind and partly brutal.

**Leverage is persistent.** Lemmon, Roberts and Zender's central finding is that a firm's leverage ratio twenty years on is forecast far better by its leverage at the start than by anything else, and that firm fixed effects absorb the majority of the variation that standard determinants were credited with. Firms do appear to have targets. They are just targets nobody can explain.

**Mean reversion is slow.** Estimated speeds of adjustment toward a fitted target vary widely with method — from under ten percent a year at the low end to around thirty percent at the high end — and the low estimates imply a half-life of well over six years, which is hard to reconcile with a costlessly re-optimized structure and easy to reconcile with the control-rights view of Chapter 21 §21.4, in which a financing mix is also an allocation of authority and therefore expensive to revise.

**Dynamic trade-off models absorb part of the drift.** The static picture asks a firm to sit at its optimum, which no firm with issuance costs would do. Make recapitalization lumpy — a fixed cost per adjustment, in the tradition Fischer, Heinkel and Zechner began — and the firm no longer holds a point but a band: it lets leverage wander with the value of its equity and refinances only when the drift becomes expensive enough to pay for. The observable consequences match the awkward facts. Leverage looks persistent because most of the time the firm is inside its band doing nothing; measured speeds of adjustment look slow because the average firm in the sample is not adjusting at all; and, as Strebulaev showed, a panel generated by a perfectly optimizing dynamic firm and then run through the standard cross-sectional regressions produces coefficients that appear to reject the very model that generated the data. That last point is a warning about method as much as a defense of the trade-off theory: a comparative static derived from a static model is not a prediction about a firm that rebalances infrequently.

**And part of the drift is not the firm at all.** Leverage measured at market has a denominator the firm does not control. Welch's point is arithmetic before it is economics: if a firm issues nothing and retires nothing, its market leverage still moves, by exactly the amount the equity market moved it, and a regression that reads the resulting series as a financing decision is fitting stock returns. Figure 23.3 puts the aggregate version of that claim next to the two measures it separates.

![Figure 23.3: Leverage is persistent and poorly explained](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-1157b167e8ae21bb6a9d31b22d900ff376bc1235%2Ffig_23_03_leverage_is_persistent.png?alt=media)

**Figure 23.3: Leverage is persistent and poorly explained.** Panel (a) is the US nonfinancial corporate sector's leverage since 1946, measured two ways from the same debt: against debt plus the market value of equity, and against assets at current cost. The first runs from about 16 percent to about 51 percent, a factor of three; the second runs from about 16 to about 25. The sector did not restructure itself three times over. Panel (b) decomposes the annual change in market leverage into the part that would have occurred with debt held fixed — the equity denominator moving on its own — and the residual, following Welch (2004). The passive component accounts for two-thirds of all the movement there is and correlates with the total change at 0.97. The findings this section reports are firm-level and the Financial Accounts are an aggregate, so the figure does not redraw Lemmon, Roberts and Zender; it draws the mechanism that makes their result unsurprising. Leverage looks persistent partly because firms have targets they return to slowly, and partly because a large share of what a leverage regression fits was produced by the stock market rather than by a financing decision. The two explanations are not rivals, and neither of them tells you what the target is. *Source: Financial Accounts of the United States (Z.1), tables L.103 and B.103, through the FRED mirror (BCNSDODNS, NCBCEL, TABSNNCB); decomposition follows Welch (2004). Author's calculations.*

**And profitability enters with the wrong sign.** This is the standing puzzle of the field, so state it precisely. The trade-off theory predicts that more profitable firms should borrow *more*: they have more taxable income to shield and a lower probability of distress at any given debt level. In the data, across every large sample and nearly every country, more profitable firms borrow *less*. The correlation between profitability and leverage is robustly negative, and Frank and Goyal's factor-by-factor audit finds it among the most reliable relationships in the entire literature. Rajan and Zingales found the same sign in every G7 country. A theory whose sharpest comparative static comes out backwards is not thereby refuted, but it does need a partner. The next section is the partner.

***

## 23.3 The Pecking Order

### The mechanics

Myers and Majluf's argument replaces the trade-off's tax-and-distress calculus with a single friction: managers know more about the firm's assets than the market does, and issuing a claim is an action that reveals what they know.

Work it once, with numbers. A firm's assets in place are worth 150 if management has seen good news and 50 if bad; the market thinks the two are equally likely, so it values the assets at 100. A project is available that costs 20 and is worth 25 gross — a net present value of 5, the same in both states — and the firm has no cash, so it must issue equity to take it.

Suppose both types issued. The post-issue firm would be worth $$100 + 25 = 125$$ to an outside investor, so twenty of new equity buys $$20/125 = 16$$ percent of the firm.

**Table 23.3: A Myers-Majluf issue-or-not decision**

|                                              | Good type (assets 150) | Bad type (assets 50) |
| -------------------------------------------- | ---------------------- | -------------------- |
| Value if the project is skipped              | 150                    | 50                   |
| True post-issue firm value                   | 175                    | 75                   |
| Old holders' stake at the pooled price (84%) | 147.0                  | 63.0                 |
| Gain from issuing at the pooled price        | **−3.0**               | **+13.0**            |

*Source: Author's calculation. Investment outlay 20, gross project value 25, pooled post-issue value 125, so new shareholders take 16 percent.*

The good type declines. Its shareholders would give up sixteen percent of a firm actually worth 175, transferring $$0.16 \times (175 - 125) = 8$$ of value to the new investors in exchange for a project worth 5. The bad type issues eagerly, for the mirror-image reason. And the market, anticipating this, does not offer the pooled price at all: knowing that only bad types issue, it values an issuing firm at 75, requiring $$20/75 = 26.7$$ percent for the same twenty — at which price the good type's shareholders retain $$0.733 \times 175 = 128.3$$ and decline even more firmly. The separating equilibrium is the one that stands, and in it the good firm forgoes a project worth five.

Two conclusions follow, and they are the theory.

**The market's markdown is the price of the friction.** Chapter 12 §12.5 reports the fact this model exists to explain: seasoned equity offerings by US industrial firms announce at roughly minus two to minus three percent. That is the empirical residue of Table 23.3's logic, diluted by the reality that firms are not cleanly separated into two types. Do not read the model's own minus fifty percent as a prediction; read the sign, and the mechanism.

**The remedy is to issue a claim whose value does not depend on what management knows.** Riskless debt is worth twenty whether the assets are 150 or 50, so issuing it transfers nothing and the good type takes the project. Retained earnings are better still, because they require issuing nothing at all. The **pecking order** follows as a *result*, not an assumption: internal funds first, then the safest external claim available, then riskier debt and hybrids, and equity last and reluctantly.

### Where it fits and where it fails

The pecking order gets three things right that the trade-off gets wrong. It explains the negative profitability-leverage correlation directly — profitable firms fund themselves internally and therefore borrow less, with no target in sight. It explains why equity issuance is rare and announces badly. And it explains the value firms place on **financial slack**: Graham and Harvey's chief financial officers rank financial flexibility and credit rating above the tax advantage of debt among their debt-policy considerations, which is the pecking order's language, not the trade-off's.

It fails in one large and well-documented place. Small, young, high-growth firms — the ones with the most severe information asymmetry, for whom the model predicts the strongest aversion to equity — are the most enthusiastic equity issuers in the economy. Frank and Goyal's tests find that net equity issuance tracks the financing deficit *better* than net debt issuance does for exactly this group, reversing the ordering the theory predicts. Shyam-Sunder and Myers's original test, which found debt absorbing nearly the whole deficit, ran on a sample of large mature firms where the prediction was least demanding.

The reconciliation usually offered is that the information problem is solved by other means at such firms: a venture capitalist's staged, contingent, control-heavy contract (Chapter 21 §21.4's last row) is a device for buying equity from an entrepreneur who knows more, and Chapter 12 §12.2's underwriter certification and analyst coverage do related work in public markets. Where the asymmetry can be contracted around, the pecking order's ordering dissolves. Where it cannot, it holds.

***

## 23.4 Market Timing as the Third Theory

Chapter 15 §15.6 routed equity market timing here, to sit beside the two theories it competes with. Its claim is more radical than either: firms have no target leverage at all, and observed capital structure is the accumulated residue of past attempts to sell claims when they were dear.

Baker and Wurgler's evidence is a single, well-designed variable. For each firm they compute an external-finance-weighted average of its historical market-to-book ratio — a measure that puts weight on the valuations prevailing at the moments the firm actually raised capital, rather than on its average valuation. That variable is strongly *negatively* related to subsequent leverage: firms that happened to raise money when their equity was expensive end up with less debt, and the relationship remains detectable a decade later. Under the trade-off theory such an effect should be arbitraged away within a couple of years by rebalancing. Under the pecking order the ordering should not depend on the market's valuation at all. Baker and Wurgler's reading is that there is nothing to rebalance toward.

That firms *try* to time is not seriously disputed. Graham and Harvey's survey found that among the considerations chief financial officers cite in deciding whether to issue equity, the amount by which their own stock is under- or overvalued ranks at or near the top — cited by roughly two thirds of respondents, ahead of most of the theoretical determinants. Chapter 12 §12.5 supplies the aggregate counterpart: issuance volume rises sharply with market valuations and the firms issuing at peaks earn poor subsequent returns. Chapter 22 §22.5 supplies the acquisition counterpart, in stock-financed acquirers who underperform.

![Figure 23.4: Market timing](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-b3e90caa2aac470c67c929ac14fc0a351ce8c818%2Ffig_23_04_market_timing.png?alt=media)

**Figure 23.4: Market timing.** The aggregate counterpart, and the reason the aggregate cannot settle the firm-level question. Panel (a) is gross issuance: the year's IPO proceeds as a share of GDP against the cyclically adjusted price-earnings ratio, 1980 to the present. The relation is what the timing story predicts — a slope of about nine hundredths of a point of GDP per point of CAPE, a correlation of +0.50, with 1999 and 2000 at the top right of the cloud and 2008 at the bottom left. Firms go public when equity is dear. Panel (b) runs the same regression on the measure the Financial Accounts publish, which is issuance *net* of repurchases and cash mergers, and the sign turns over. The two panels are not in tension and the second is not a refutation of the first. Firms issue equity when the market is dear and they also retire equity when the market is dear, and a net measure differences those two decisions away: 1999 and 2000 sit at the far right of panel (b) with net issuance of about −1 percent of GDP, because the same valuations that pulled companies to the IPO window pulled other companies into the buyback. The timing claim is a claim about the issuance decision, so the series that nets it against the repurchase decision cannot test it. That is the aggregate form of the identification problem Leary and Roberts raise at the firm level, and it is why the evidence in this section is firm-level evidence. *Source: Jay Ritter's IPO statistics (University of Florida), Robert Shiller's ie\_data.xls, and the Financial Accounts of the United States through the FRED mirror, with GDP from the same source. Author's calculations.*

The critique is about **persistence**, and it is serious. Leary and Roberts show that a firm which does nothing at all after an issuance — no rebalancing, but also no active timing — will display a mechanically persistent leverage effect simply because equity issuance mechanically lowers leverage and returns accumulate on the equity; distinguishing genuine timing from passive drift requires modeling the adjustment process, and once that is done the evidence for a *permanent* effect weakens considerably. Alti, using hot-market initial public offerings as a cleaner timing event, finds a large impact on leverage that reverses within about two years. Others argue the external-finance-weighted market-to-book variable is proxying for growth opportunities, which have their own claim on leverage. The honest summary is that firms time, that timing moves leverage, and that how long the move survives is unsettled.

There is a deeper question underneath, and it connects to Chapter 7. Timing requires that prices be predictably wrong and that managers know it — the same joint claim Chapter 7 §7.4's predictability debate could not settle from the outside, here asserted from the inside by the people with the best information about the asset.

***

## 23.5 Payout

### The irrelevance baseline

Miller and Modigliani's 1961 dividend paper is the same argument in the other direction. Hold investment policy fixed. A dollar paid out is a dollar not retained, so the share price falls by the dividend on the ex-date; a shareholder who wants cash and receives none can sell shares, and one who receives an unwanted dividend can buy more. **Homemade dividends** replicate any payout policy the firm might choose, so payout policy cannot matter. The frictions are the whole subject, and there are three.

### Taxes and clienteles

If dividends and capital gains are taxed differently, the two forms of payout are not the same claim, and holders in different tax positions rank them differently.

Take a firm with a thousand shares at fifty and five thousand of cash to distribute. Paid as a dividend, that is five per share and the price goes ex at forty-five. Used to repurchase, it retires a hundred shares at fifty, leaving nine hundred shares against forty-five thousand of value — a price of fifty, unchanged. Now follow three holders of a hundred shares each, at a cost basis of thirty, with dividends and long-term gains both taxed at 23.8 percent.

**Table 23.4: Dividend versus repurchase, three holders**

| Holder                                   | Wealth after a dividend | Wealth after a repurchase | Difference |
| ---------------------------------------- | ----------------------- | ------------------------- | ---------- |
| Taxable, sells pro rata into the buyback | 4,881.0                 | 4,952.4                   | +71.4      |
| Taxable, does not sell                   | 4,881.0                 | 5,000.0                   | +119.0     |
| Tax-exempt (pension, endowment)          | 5,000.0                 | 5,000.0                   | 0.0        |

*Source: Author's calculation. One thousand shares at 50, a distribution of 5,000, a cost basis of 30 per share, and a 23.8 percent rate on both dividends and realized long-term gains.*

Three readings, in order of importance. The repurchase advantage for the participating holder is exactly $$0.238 \times 300 = 71.4$$ — the tax saved on the *basis* returned, which a dividend taxes in full and a sale does not. The non-selling holder does better still, because the buyback lets him defer indefinitely: a repurchase is a payout that only the holders who want it pay tax on. And the tax-exempt holder is indifferent, which is the point of the third row. Pension funds, endowments, and foreign holders under treaty rates do not share the taxable holder's preference at all, and Chapter 16 shows how much of the market they are.

That is a **clientele**: firms with different payout policies attract different holders, and once the sorting has happened, a change in policy imposes a cost on the holders who sorted in. Chapter 14 §14.5's asset-location logic is the household side of the same arithmetic, and Chapter 10 §10.7's municipal-bond puzzle is the purest version of it — a claim whose price is set entirely by the tax status of whoever is marginal.

**Dividend-tax capitalization** is the pricing counterpart. If a dollar of dividend is taxed at $$\theta\_d$$ and a dollar of capital gain at $$\theta\_e$$, the ex-day price should fall by $$(1-\theta\_d)/(1-\theta\_e)$$ per dollar of dividend — less than the full dividend when dividends are taxed more heavily, which is what Elton and Gruber found and read as revealing the marginal holder's tax rate. The inference has been contested for as long as it has stood, because short-horizon traders face different effective rates than long-horizon holders, and because tick sizes and transaction costs bound the arbitrage. What survives the contest is the direction, not a point estimate of anyone's tax rate.

### Signaling and smoothing

Dividends are sticky in a way that no frictionless model generates. Lintner's interviews with corporate managers produced the model that still fits: firms have a target payout ratio, and move only part of the way toward it each year,

$$
\Delta\mathrm{Div}\_t = a + \mathrm{SOA}\times\left(\mathrm{POR}\times\mathrm{EPS}\_t - \mathrm{Div} \_{t-1}\right),
$$

with an adjustment speed $$\mathrm{SOA}$$ that Lintner estimated near a third. Run it at $$\mathrm{SOA} = 0.3$$, from a firm with a target payout ratio of one half and a prior dividend of fifty. If earnings jump by half, from a hundred to a hundred and fifty, the dividend rises only to 57.5 — a payout of 38 percent against a target of 50. If instead earnings fall by a fifth, to eighty, the dividend is cut only to forty-seven, a payout of 59 percent. In both directions the dividend moves a fraction of the way and the payout ratio absorbs the rest. Dividends follow earnings with a long lag and a heavy hand.

Why? The signaling account says a dividend is credible because it is costly to sustain and humiliating to cut, so only firms confident of their cash flows commit to one — and the announcement evidence agrees in sign, with increases greeted positively and cuts punished severely. The account has always struggled with magnitude: for a dividend to be a costly signal, the tax cost must exceed the benefit of mimicry, and the numbers do not obviously work. Brav, Graham, Harvey and Michaely's survey found managers describing something blunter and more convincing: they treat the existing dividend as nearly as inviolable as an investment commitment, and report they would sooner raise external finance or pass up a positive-net-present-value project than cut it. That is not a signal being sent. It is a constraint being obeyed, and the constraint exists because the market has learned to read cuts as catastrophic.

### The rise of the buyback

Repurchases were rare before the 1980s, and *gross* repurchases are now the dominant form of US corporate payout — a fact that lives in the S\&P and Compustat compilations rather than in the Financial Accounts, which publish only the net measure Figure 23.5 draws. Three forces, in the order of their contribution. A 1982 SEC safe harbor made open-market repurchases legally routine rather than a manipulation risk. The tax advantage of Table 23.4 is permanent and applies to every taxable holder. And flexibility is the decisive one: a repurchase authorization is an option, not a promise, and firms cut buybacks sharply in downturns without any of the consequences a dividend cut carries. Fama and French documented the flip side as "disappearing dividends" — the share of listed US industrial firms paying any dividend fell by roughly two thirds between the late 1970s and the end of the 1990s. Chapter 12 §12.6 carries the aggregate fact this produces, and it is the striking one: net equity issuance by US nonfinancial corporations has been persistently negative since the mid-1980s. The stock market is where firms return money, not where they raise it. A one percent excise tax on net repurchases, effective in 2023, is the first material change to the calculus in four decades and is too recent to evaluate.

![Figure 23.5: Dividends and repurchases](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-366dc9bb5f80cdd936953d60fcf562465413614a%2Ffig_23_05_dividends_and_repurchases.png?alt=media)

**Figure 23.5: Dividends and repurchases.** The two forms of payout by US nonfinancial corporations, annually since 1950. Dividends grow with the sector and almost never fall — Lintner's smoothing, visible as a line with no cliffs in it. Net equity retirement is flat at nothing until the early 1980s, turns positive within two years of the safe harbour, and reaches 635 billion dollars in 2022 alone. It is also volatile in a way the dividend line never is, collapsing in 2009 and again in 2020 and recovering within a year, which is the flexibility §23.5 identifies as the decisive advantage: an authorization is an option and a dividend is a promise. One caution the figure makes unavoidable. This is *net* equity retirement — gross repurchases less gross issuance less equity retired for cash in mergers, which is what the Financial Accounts publish. It has exceeded the dividend in eight years since 1984 but not on average, and the gap is informative rather than a measurement failure: a large part of gross repurchase activity offsets shares issued under employee compensation plans rather than returning cash to outside holders. Chapter 12 §12.6 reads the same series for what it says about issuance. *Source: Financial Accounts of the United States (Z.1), net dividends paid and net issues of corporate equities by nonfinancial corporate business, via the FRED mirror; author's calculations.*

### Payout and governance

Jensen's free-cash-flow argument inverts the question. If managers of mature, cash-generating firms in industries with poor reinvestment opportunities would rather build empires than return money, then payout is not a distribution decision but a discipline: it removes the resources that would otherwise be wasted, and forces the firm back to the capital market for its next dollar, where it must justify itself. Debt does the same work harder, because the obligation is contractual rather than discretionary, which is why the leveraged buyout of a mature cash cow is the free-cash-flow theory's natural experiment and why Chapter 22 §22.6's 1980s hostile bidders targeted the profile they did. The other side of the argument is that discretion is worth something too, and firms that pay out everything have no slack when the good project arrives — which is §23.3's point restated. Who decides, under what contractual constraint, is Chapter 24 §24.2, which takes Jensen and Meckling's apparatus — named and deferred at Chapter 21 §21.5 — and deploys it.

> **Box 23.1 — Rule 10b-18, in four conditions**
>
> Section 23.5 dispatches the legal status of repurchases in a sentence. The rule is worth four lines of its own, because its structure is the reason an authorisation is an option and a dividend is a promise.
>
> Rule 10b-18, adopted by the Securities and Exchange Commission in 1982, provides a **safe harbour**: an issuer that repurchases its own shares in compliance with four conditions on a given day will not be deemed, solely by reason of the manner, timing, price or volume of those purchases, to have violated the general anti-manipulation provisions. The conditions are these.
>
> **Manner.** All of the day's repurchases must be effected through a single broker or dealer.
>
> **Timing.** Purchases must not be the opening transaction, and must not be made in the closing minutes of the session — a window that is wider for less actively traded securities than for the most liquid ones.
>
> **Price.** No purchase may be made above the higher of the last independent transaction price and the highest independent published bid.
>
> **Volume.** The day's purchases must not exceed a stated fraction of the security's average daily trading volume, with an exception for one block purchase in place of the day's other buying.
>
> Two features of that structure matter more than the numbers. It is a safe harbour rather than an exemption: a repurchase outside the conditions is not unlawful, it merely loses the presumption, which is why the conditions function as a code of practice rather than a boundary. And nothing in the rule obliges an issuer to buy anything. A board authorises a repurchase programme of a stated size, and the programme is an option the company may exercise, reduce, or quietly abandon.
>
> That asymmetry is §23.5's whole point about the signalling content of payout. A dividend cut is an announcement; a repurchase not executed is a non-event nobody has to report. Chapter 12 §12.6 uses the same rule from the issuance side.

***

## 23.6 What the Evidence Supports

The honest summary is short and unflattering to all three theories.

**Leverage is persistent and poorly explained.** Frank and Goyal's audit of the determinants finds six factors that survive across specifications and samples: median industry leverage, asset tangibility, firm size, and expected inflation enter positively; market-to-book and profitability enter negatively. Together they account for a modest fraction of the cross-sectional variation, and Lemmon, Roberts and Zender's fixed effects absorb far more than the observables do. Something stable and firm-specific is setting leverage, and it is not in the standard regressors.

**★ And the dependent variable is contested.** Before crediting or blaming any theory for the fit, ask what "leverage" was measured as. Welch's objection is that the standard ratio is built badly in two ways. Non-financial liabilities — accounts payable, pension obligations, deferred taxes — sit in the denominator of the usual debt-to-assets measure but are not financing choices, so a firm that stretches its payables is recorded as having deleveraged. And book leverage and market leverage are different dependent variables: because the market value of equity moves far more than anything the firm does, a market-leverage regression is substantially a regression on past stock returns, which is how a mechanical channel can masquerade as a capital structure decision and is the same objection Leary and Roberts direct at the persistence results of §23.4. The profitability sign is where this bites hardest, since a profitable firm's equity value rises whether or not it has issued or retired a security. None of this makes the negative correlation disappear. It does mean that some fraction of the literature's most reliable finding is a statement about the denominator.

**The three theories are lenses, not laws, and their errors are complementary.** Trade-off gets the profitability sign wrong and gets tangibility, size, and industry effects right. Pecking order gets profitability right and gets the equity-hungry growth firm wrong. Market timing explains why leverage looks like a history rather than a target and cannot say what firms would do if prices were always right. A reader who wants one theory should ask which friction dominates for the firm in front of them: a mature tangible-asset firm with a stable tax position is a trade-off firm, an opaque mid-size firm is a pecking-order firm, and a firm whose equity has just tripled is a timing firm.

**Identification has settled less than the citation counts suggest.** The cleanest evidence comes from tax changes that vary across firms for reasons unrelated to their financing. Studies exploiting staggered US state corporate income tax changes find leverage responds in the predicted direction but modestly, and — the more interesting finding — asymmetrically: leverage rises after tax increases considerably more than it falls after cuts, which no symmetric trade-off model produces. Cross-country reform evidence points the same way on sign and magnitude. What these designs establish is that the tax channel is real and second-order in size. What they cannot establish is the counterfactual the trade-off theory is actually about, since none of them observes distress costs. The 2017 US reform, which cut the corporate rate and simultaneously capped interest deductibility, is the largest recent experiment and its effects are still being estimated; the data exercise puts the reader in front of it.

***

## 23.7 Who Holds the Firm's Debt, and What Their Constraints Do to Its Price

Every chapter of Parts II, III, and V asks who holds the claim and what their constraints do to its price. Part V's version of the question has the arrow reversed, and this section is where the reversal is made explicit: if holders' demand curves are steep, and Chapter 20 established that they are, then the *composition* of what firms issue is determined in part by what holders are short of.

**Gap-filling.** Greenwood, Hanson and Stein made the argument precise on the debt-maturity margin. The government is the largest issuer of long-dated claims and it does not choose its maturity structure with reference to corporate financing. When the Treasury lengthens — issuing more long bonds and fewer bills — the supply of long-duration claims available to the habitat investors of Chapter 9 §9.5 rises, long yields cheapen relative to short, and corporations respond by shortening their own issuance. When the Treasury shortens, firms lengthen. Their estimated relationship is significantly negative, economically substantial, and — the detail that establishes the mechanism — concentrated among large, unconstrained, investment-grade issuers. Small firms cannot arbitrage a maturity gap; the firms with standing shelf registrations and a choice of tenor can, and do. Corporate maturity choice becomes, on this evidence, a predictor of excess bond returns: firms are on the profitable side of the term premium because they are the ones filling the gap. This is the corporate-side counterpart of Chapter 9 §9.5's preferred habitat, with the issuer playing the arbitrageur.

![Figure 23.6: The supply the gap-fillers fill](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-03e9013fa52ede1ce48d5220d8c77fe700c190ee%2Ffig_23_06_the_supply_the_gap_fillers_fill.png?alt=media)

**Figure 23.6: The supply the gap-fillers fill.** The long share of marketable Treasury debt — everything that is not a bill — since 1945, with Greenwood, Hanson and Stein's 1963-2005 estimation window shaded. This is the right-hand side of their regression, and the figure draws it alone. The variation is large: from 54.2 percent at the 1975 trough, after a decade of deficits financed heavily at the short end, to 89.4 percent in 2015, after the Treasury had spent the post-crisis years deliberately extending the average maturity of the debt — 26 points of movement inside the shaded window alone. What matters for the argument is *why* it moves. War finance, deficit swings, debt-management doctrine, and the bill surges of 2008-09 and 2020 are the reasons, and not one of them is corporate financing. That is the exogeneity the gap-filling test requires, drawn rather than asserted. The corporate half is not drawn, and the reason is worth stating rather than hiding. Greenwood, Hanson and Stein measure the long-term share of *gross* corporate issuance, and no free aggregate does: the Financial Accounts publish issuance net, which destroys the signal twice over. A firm rolling a maturing bond into commercial paper has made exactly the maturity choice the theory is about, and it nets to roughly zero; and one firm shortening cancels another lengthening before the aggregate is struck. The estimated response reported in the text is therefore theirs, established on security-level data this figure cannot substitute for. Data exercise 13 builds the missing half. *Source: Financial Accounts of the United States (Z.1) via the FRED mirror. Author's calculations.*

**Safe-asset supply.** The same logic on the safety margin rather than the maturity margin. Chapter 9 §9.4 measures a convenience yield: money-like claims trade rich because they render a service beyond their cash flows, and the size of the premium moves with the quantity of Treasuries outstanding. A premium on near-money is an invitation to manufacture near-money, and the private sector accepts it. When Treasury supply is scarce, the financial sector expands its issuance of short-term, money-like liabilities; asset-backed commercial paper volumes track the money-like premium; and the pre-2008 machine for converting mortgages into AAA tranches was, in this reading, safe-asset manufacture responding to a price. Nonfinancial corporations participate at the safe end of the same market — a highly rated firm issuing short paper into a shortage of high-grade collateral is supplying a scarce good, and the spread it pays is what tells it so.

**Credit-supply effects on leverage.** The third mechanism runs directly at leverage, and it is the demand curve dragging the supply curve. When the holders of Chapter 10 §10.9 — insurers whose risk-based capital schedule is nearly flat within investment grade, and who therefore reach for yield inside the buckets — expand their appetite for corporate credit, spreads compress and firms lever up. The identification here is good, because access to credit supply varies for reasons unrelated to any firm's own demand for it. Firms with a credit rating, and therefore access to the public bond market, carry substantially more debt than otherwise comparable unrated firms. When the high-yield market collapsed in 1989-90 after Drexel's failure and the forced divestment of below-investment-grade holdings by thrifts, speculative-grade firms cut net debt issuance and did not fully substitute into other sources — a supply shock, not a change in anyone's target. The trade-off theory's optimum is drawn as if the supply of credit were a horizontal line at a price. It is not; it is a demand curve belonging to a small number of very large, constrained holders, and it moves.

**Apple, resolved.** Return now to April 2013 with all three mechanisms in hand. The company sold seventeen billion dollars of highly rated paper across six maturities into a market in which the safe-asset shortage of Chapter 9 §9.4 was acute, the reaching-for-yield behavior of Chapter 10 §10.9 was documented, and the liability-driven demand for duration of Chapter 16 §16.2 was unsatisfied at the long end. Every one of those holders wanted exactly what Apple could manufacture: a large, liquid, index-eligible, high-grade claim in size, at maturities where the alternatives were scarce. The tax wedge explains why the firm wanted to borrow rather than repatriate; the activist pressure explains why the cash had to move at all; but the *terms* — the spread, the size, the tranching across three, five, ten and thirty years — were set by whose demand was unmet. Apple did not go to the bond market because it needed capital. It went because the price of the claim it could issue was, for a moment, extraordinarily high, and issuing it was the cheapest way to satisfy the holders of its equity.

Which is Part V's thesis in its most compact form. Firms are not passive recipients of a cost of capital handed to them by Chapter 22's formula. They are manufacturers, and they manufacture what is dear. Two questions remain for this part. Chapter 24 asks who inside the firm decides which claim to issue, and by what contractual authority — because a capital structure is also a control-rights allocation, and someone had to be in a position to change it. Chapter 25 asks which firms actually get to play this game at all, since everything in this section required a shelf registration, an investment-grade rating, and a bond market that returns a call — and most firms in any economy have none of the three.

In Chapter 1 §1.2's terms, the price at which a firm can sell a bond reports a flow meeting a constraint binding far more often than it reports news, which is why Apple's spread in April 2013 was a statement about insurers' capital charges and habitat demand rather than about Apple.

> **Box 23.2 — Drexel, February 1990**
>
> Section 23.7 argues that the supply of credit is a determinant of capital structure and not merely a price. The cleanest natural experiment for that claim is the closing of one market by two unrelated events eighteen months apart.
>
> The first was regulatory. The Financial Institutions Reform, Recovery, and Enforcement Act of 1989 — passed to resolve the savings and loan crisis — required thrifts to divest their holdings of below-investment-grade corporate bonds over a stated period. Thrifts had been substantial buyers of high-yield debt, and the statute converted a large class of holders into forced sellers on a schedule known to everyone.
>
> The second was the failure of the market's principal dealer. Drexel Burnham Lambert, which had built the modern high-yield market and remained its dominant underwriter and market maker, filed for bankruptcy protection in February 1990 after losing access to short-term funding. The market did not merely lose a firm. It lost the balance sheet that had stood between buyers and sellers, at the moment a statute was manufacturing sellers.
>
> New high-yield issuance collapsed, and the interesting question is what the affected borrowers did about it. The finding §23.7 uses is that speculative-grade issuers reduced net debt and did not substitute into other sources — not bank loans, not equity, not private placements. A firm cut off from the one door it was eligible for did not walk to another door. It shrank its balance sheet.
>
> That is what a credit-supply effect looks like when it is identified rather than asserted. The shock is to the *holder* — a statute that changed who was permitted to own the claim, and a bankruptcy that removed who was willing to warehouse it — and nothing about the issuing firms' investment opportunities moved with it. Chapter 25 §25.3's account of what happens when bank credit contracts is the same experiment run on a different door.

***

## Elsewhere in the Series

* **Aggregate corporate financial structure and its macroeconomic consequences** — *Institutionalist Macroeconomics*, which owns the leverage cycle as a macro object; this chapter owns the firm-level financing decision that aggregates into it.
* **This book**: linearity of prices, which is what the irrelevance proof actually uses — Chapter 3 §3.2. Leverage constraints that stop investors manufacturing homemade leverage — Chapter 4 §4.9. Equity as an option on firm value, behind risk-shifting and debt overhang — Chapter 8, and Chapter 10 §10.2's structural model. The convenience yield on near-money claims, and preferred habitat — Chapter 9 §§9.4-9.5. Insurers as the marginal holder of corporate credit, and municipal bonds as the purest tax clientele — Chapter 10 §§10.7, 10.9. Seasoned-offering markdowns, the market-timing evidence, and buybacks as the source of the negative net issuance number — Chapter 12 §§12.5-12.6, 12.9. Household tax environments and asset location — Chapter 14 §14.5. Behavioral corporate finance, routed here — Chapter 15 §15.6. Regulatory capital schedules and liability-driven duration demand — Chapter 16 §16.2. Demand elasticities and the price multiplier this chapter's §23.7 supplies the supply side for — Chapter 20 §20.3. A security as an allocation of cash-flow and control rights — Chapter 21 §21.4. The WACC that consumes this chapter's tax shield, and method-of-payment evidence in acquisitions — Chapter 22 §§22.1, 22.5. Covenants, boards, and the agency machinery §23.5 gestures at — Chapter 24 §§24.1-24.3. What firms actually issue, and which firms can — Chapter 25 §§25.1, 25.3.

***

## Summary

1. **Modigliani-Miller Proposition I is a replication argument, not an equilibrium condition.** Debt and equity partition the firm's payoff; by the linearity of prices established in Chapter 3 §3.2, the parts must sum to the whole. Homemade leverage is the trade that enforces it: a mispriced levered firm yields five today per one percent, forever, at zero risk.
2. **Proposition II is bookkeeping, not a result.** Leverage raises the cost of equity by exactly the amount that leaves the weighted average unchanged: $$r\_E = r\_U + (D/E)(r\_U-r\_D)$$ takes 10 percent to 13.33 percent at a leverage ratio of 40 percent, and the WACC stays at 10.
3. **What the proof assumes is the chapter's map** (Table 23.1). Taxes, distress costs, information, timing, incentives, and segmented holders are the six failure conditions, and each is a section or a pointer. The compact statement: slicing the claim bundle changes nothing unless a slice changes taxes, incentives, information, or who can hold it.
4. **The tax shield is** $$\tau\_c D$$ **only under three conditions**: permanent debt discounted at the cost of debt, taxable income to shield, and no offsetting personal-tax wedge. Discounting the same shield at the unlevered cost of capital halves it.
5. **Personal taxes make the gain from leverage depend on who holds the bond** (Table 23.2). At $$\tau\_c = 21$$ percent with a high-bracket taxable bondholder the gain is negative; with a tax-exempt marginal bondholder it is about a third of a dollar per dollar of debt — larger than $$\tau\_c$$ itself.
6. **Direct bankruptcy costs are small; the costs that matter are indirect.** Fees run to low single-digit percentages of value. Andrade and Kaplan's separation of financial from economic distress puts the total at something on the order of ten to twenty percent of firm value, alongside debt overhang and risk-shifting, which bite long before default.
7. **Leverage is persistent, mean-reverts slowly, and correlates negatively with profitability.** The last is the standing puzzle: the trade-off theory predicts the opposite sign, and the negative correlation appears in every large sample and every G7 country.
8. **Myers-Majluf delivers the pecking order as a result** (Table 23.3). A good-type firm declines a project worth 5 rather than transfer 8 to new shareholders; the market anticipates this and marks issuers down. The remedy is to issue the claim whose value is least sensitive to private information, which orders internal funds, then debt, then equity.
9. **The pecking order fails where the asymmetry can be contracted around.** Small, young, high-growth firms — the model's worst case — issue equity most enthusiastically, because staged venture contracts and underwriter certification substitute for the information the market lacks.
10. **Market timing says there is no target to revert to.** Baker and Wurgler's external-finance-weighted market-to-book ratio predicts leverage a decade out; two thirds of chief financial officers say their own valuation is a first-order consideration in issuing equity. The persistence result is contested — Leary and Roberts's mechanical channel and Alti's two-year reversal are the sharpest objections.
11. **Payout irrelevance is the same replication argument** (Miller-Modigliani 1961): homemade dividends undo any policy the firm picks, so the frictions are taxes, signaling, and governance.
12. **The repurchase advantage is exactly the tax on the basis returned** (Table 23.4): 71.4 for a participating taxable holder, 119.0 for one who does not sell, and zero for a tax-exempt holder — which is what makes payout a clientele phenomenon.
13. **Dividends are smoothed to the point of rigidity.** Lintner's partial-adjustment rule with a target payout of one half and a speed of 0.3 takes a dividend from 50 only to 57.5 when earnings rise by half, and cuts it only to 47 when earnings fall by a fifth — the payout ratio absorbing the difference in both directions. Managers describe the level as nearly as binding as an investment commitment.
14. **Buybacks won on tax and flexibility.** A 1982 safe harbor, the tax advantage of Table 23.4, and the fact that an authorization is an option rather than a promise, together with the disappearance of dividend payers, produce the persistently negative net equity issuance of Chapter 12 §12.6.
15. **No single theory explains leverage, and their errors are complementary.** Six factors survive Frank and Goyal's audit and explain a modest share of the variation; firm fixed effects explain far more. Tax-change natural experiments find real but second-order effects, and an asymmetry — leverage rises after increases more than it falls after cuts — that no symmetric model produces.
16. **Issuance responds to holder demand.** Firms fill maturity gaps left by government issuance (Greenwood-Hanson-Stein), manufacture near-money when the convenience yield is high, and lever up when credit supply expands for reasons unrelated to their own demand. Apple's 2013 bond sale is all three at once: a claim manufactured because its price, for a moment, was extraordinarily high.

***

## Key Terms

* **Modigliani-Miller irrelevance**: The proposition that a firm's total market value is independent of how its payoff is divided into securities, proved by replication from the linearity of prices rather than assumed
* **Homemade leverage**: An investor's manufacture of a levered (or unlevered) payoff by borrowing (or lending) on personal account, which is the trade that enforces irrelevance and the operation constrained holders cannot always perform
* **Tax shield**: The present value of the tax saved by deducting interest, equal to $$\tau\_c D$$ for permanent debt discounted at the cost of debt, and materially smaller under rebalancing, limited taxable income, or an offsetting personal-tax wedge
* **Distress costs**: The resources consumed by, and the decisions distorted in anticipation of, financial distress — direct fees, which are small, and indirect costs including customer and supplier flight, debt overhang, and risk-shifting, which are not
* **Trade-off theory**: The account in which an interior optimal leverage ratio equates the marginal tax shield to the marginal expected cost of distress, predicting targets, mean reversion, and a positive profitability-leverage relation that the data reverse
* **Pecking order**: The financing hierarchy — internal funds, then debt, then equity — that follows from Myers and Majluf's adverse-selection problem rather than being assumed
* **Adverse selection (in issuance)**: The transfer from existing to new shareholders when a firm with favorable private information issues equity, which makes such firms decline positive-net-present-value projects and makes the market mark down every issuer
* **Market timing**: The account in which capital structure is the cumulative residue of past attempts to issue claims when they were expensive, with no target to revert to
* **Payout smoothing**: The Lintner pattern in which dividends adjust only partially toward a target payout ratio each year, producing a dividend series far less volatile than earnings
* **Clientele**: A group of holders whose tax position, mandate, or horizon makes one form of payout or one type of claim strictly preferable, so that a change in firm policy imposes a cost on the holders who sorted in
* **Gap-filling**: The finding that firms adjust the maturity and type of the claims they issue to fill the gaps that government issuance and holder demand leave, concentrated in the large, unconstrained issuers able to act on the spread

***

## Readings

### Required

* Modigliani, F. and M. H. Miller (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment." *American Economic Review* 48(3): 261-297. *Read the arbitrage argument in Section I and skip nothing else that is not algebra: the paper's lasting contribution is a method — replication, later Chapter 3's — applied to a question everyone had been answering with accounting intuition. The assumption list is the field's research agenda for the following sixty years.*
* Myers, S. C. and N. S. Majluf (1984). "Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have." *Journal of Financial Economics* 13(2): 187-221. *The pecking order derived rather than asserted. Note that the result is about underinvestment, not about a preference ordering over securities: the ordering is what the underinvestment problem implies, and the paper is careful about the difference in a way most secondary accounts are not.*

### Recommended

* Baker, M. and J. Wurgler (2002). "Market Timing and Capital Structure." *Journal of Finance* 57(1): 1-32. *The third theory, and a lesson in variable construction — the external-finance-weighted market-to-book ratio is what makes the test sharp. Read the persistence results with Leary and Roberts's mechanical-drift objection in hand.*
* Greenwood, R., S. Hanson and J. C. Stein (2010). "A Gap-Filling Theory of Corporate Debt Maturity Choice." *Journal of Finance* 65(3): 993-1028. *The supply-side counterpart of this book's demand system, and the paper §23.7 is built on. The concentration of the effect among large, unconstrained issuers is the identifying detail; the excess-return prediction is the payoff.*
* Lintner, J. (1956). "Distribution of Incomes of Corporations Among Dividends, Retained Earnings and Taxes." *American Economic Review* 46(2): 97-113. *A survey of managers that produced a partial-adjustment equation still fitting seventy years later. Worth reading as evidence that asking people what they do is a legitimate research method when the alternative is inferring it from an equilibrium condition.*
* Easterbrook, F. H. (1984). "Two Agency-Cost Explanations of Dividends." *American Economic Review* 74(4): 650-659. *The missing anchor for §23.5's governance material: a dividend forces the firm back to the capital market, where new investors and their underwriters perform the monitoring that dispersed existing shareholders will not. Payout as a governance device rather than a tax puzzle.*
* Graham, J. R. and C. R. Harvey (2001). "The Theory and Practice of Corporate Finance: Evidence from the Field." *Journal of Financial Economics* 60(2-3): 187-243. *Also assigned in Chapter 22. For this chapter, read the debt-policy and equity-issuance sections: financial flexibility and credit rating outrank the tax shield, and stock valuation outranks most theoretical determinants of equity issuance.*
* Frank, M. Z. and V. K. Goyal (2009). "Capital Structure Decisions: Which Factors Are Reliably Important?" *Financial Management* 38(1): 1-37. *The audit §23.6 relies on. Six factors survive; the explanatory power is modest; and the profitability sign is where every theory in the chapter has to be confronted with the data.*
* Welch, I. (2011). "Two Common Problems in Capital Structure Research: The Financial-Debt-to-Asset Ratio and Issuing Activity versus Leverage Changes." *International Review of Finance* 11(1): 1-17. *The measurement objection behind §23.6's starred paragraph, circulated for years under the blunter working title "Why I Do Not Understand Capital Structure Research." Read it before running any leverage regression of your own; the argument is about the denominator and about what a market-leverage change actually records.*
* Miller, M. H. (1991). "Leverage." *Journal of Finance* 46(2): 479-488. *The Nobel lecture, and a first-person account of what the 1958 proof was and was not claiming. Read it for the treatment of the tax correction and of the leverage-and-financial-stability debate, on which Miller is more careful than the literature that cites him.*
* Myers, S. C. (2001). "Capital Structure." *Journal of Economic Perspectives* 15(2): 81-102. *The retrospective from the author of the pecking order, twenty pages and no algebra. The best bridge between §23.2 and §23.3 for a reader not yet ready for Myers-Majluf, and unusually candid about how little the three theories jointly explain.*
* Allen, F. and R. Michaely (2003). "Payout Policy." In *Handbook of the Economics of Finance*, Volume 1A. Elsevier. *The survey §23.5 lacks one of its own. Comprehensive on the taxes, signaling, and clientele evidence, and it predates the full repurchase transition, which makes it useful for seeing which of the old dividend puzzles the transition disposed of and which it did not.*
* Villamil, A. P. (2008). "Modigliani-Miller Theorem." In *The New Palgrave Dictionary of Economics*, 2nd edn. Palgrave Macmillan. *Four pages stating the proposition and its assumption list. The ideal thing to read before §23.1 rather than after, because it separates the theorem from the sixty years of commentary attached to it.*
* Bolton, P. and F. Samama (2012). "Capital Access Bonds: Contingent Capital with an Option to Convert." *Economic Policy* 27(70): 275-317. *A worked security design aimed at one row of Table 23.1, and the concrete case for §23.1's claim that the assumption list is a research agenda. Read with Chapter 19 §19.2 on bank capital and Chapter 8 on the option the conversion trigger creates.*

***

## Discussion Questions

1. **The profitability puzzle.** More profitable firms borrow less, in every large sample and nearly every country, and the trade-off theory predicts the opposite. Set out what each of the chapter's three theories predicts for the profitability-leverage relation and why. Then consider three defenses of the trade-off theory: that leverage is measured as a ratio whose denominator rises mechanically with profitability; that adjustment costs mean firms are observed away from their targets; and that profitability proxies for growth opportunities, which carry their own effect on leverage. For each, state what additional evidence would confirm or kill it — and say whether any defense, if successful, would leave the trade-off theory with content it did not already borrow from elsewhere.
2. **Was Apple's 2013 structure optimal, or induced?** Two readings of the opening episode. Under the first, management solved a well-posed problem: given the repatriation wedge, borrowing against foreign cash to fund a domestic payout was cheaper than the alternative, and the activists merely accelerated a decision that was correct anyway. Under the second, the structure was induced by holders — the payout size was set by what it took to end a public campaign, and the debt was issued because a demand shortage made it temporarily cheap, neither of which is an optimum in any of §§23.2-23.4's senses. Build both cases. What evidence would distinguish them, given that both predict the same observed transaction? Then ask the harder question: if a capital structure is negotiated with holders rather than chosen by managers, whose objective function is it optimizing, and does the trade-off theory have anything to say about the answer?
3. **Does the pecking order survive its counterexample?** The firms with the worst information asymmetry issue the most equity. Three reconciliations appear in §23.3: contracting around the asymmetry, certification by intermediaries, and the possibility that debt capacity binds first for firms with no tangible assets. Which of these is a rescue of the theory and which is a replacement of it? Design an empirical test using variation in the availability of venture capital or in underwriter reputation, and say what result would make you abandon the pecking order rather than qualify it.
4. **Buybacks, flexibility, and what was lost.** The shift from dividends to repurchases is usually explained by tax and flexibility, and §23.5 endorses both. But flexibility is exactly what Jensen's free-cash-flow argument says should *not* be granted to managers of mature firms: a dividend is a commitment and a buyback authorization is not. Argue that the shift to buybacks was a governance regression. Then argue that it was a governance improvement, using the fact that a repurchase concentrates ownership among the holders who choose to stay. Which argument does the evidence on payout announcement returns bear on, and which does it not touch?
5. **Whose tax rate is in the shield?** Table 23.2's last row makes the gain from leverage larger than $$\tau\_c$$ when the marginal bondholder is tax-exempt. Roughly what fraction of US corporate bonds are held by holders outside the personal income tax net — pensions, retirement accounts, foreign official and private holders, and insurers' tax-favored accounts? Use Chapter 2's master holdings table and Chapter 10 §10.9. If that fraction is large and has been rising, what should have happened to aggregate corporate leverage over the same period, and did it? What else changed at the same time that would confound the inference?

***

## Problems

**Problem 1 — Homemade leverage and an arbitrage.** Firm U is all equity, with a perpetual expected operating cash flow of 1,000 per year and a market value of 10,000. Firm L has identical assets, plus 4,000 of riskless perpetual debt at 5 percent. There are no taxes and no distress costs.

(a) Compute Firm L's equity value, the expected cash flow to its equity, and its cost of equity. Verify Proposition II and verify that both firms have the same weighted average cost of capital.

(b) An investor has 6,000 and wants Firm L's equity return but can buy only Firm U. Describe the position and verify that its payoff and return match L's equity exactly.

(c) An investor holds one percent of L's equity and wants Firm U's return without owning U. Describe the position and verify its cost and payoff.

(d) The market now prices L's equity at 6,500. Construct an arbitrage using one percent of each claim. Report the cash received today and the net cash flow in every subsequent year, and state what forces the mispricing to close.

(e) Name two features of a real institutional investor that would prevent it from executing the trade in (d), and say for each whether it makes $$V\_L$$ more likely to exceed or to fall short of $$V\_U$$.

**Problem 2 — The tax shield, with and without personal taxes.** Use Firm U and Firm L from Problem 1, now with a corporate tax rate of 21 percent.

(a) Compute the annual interest tax saving and the value of the tax shield, assuming permanent debt and a discount rate equal to the cost of debt. Report $$V\_L$$ and L's equity value.

(b) The firm instead maintains a constant target debt *ratio*, so future debt levels move with firm value. Argue that the appropriate discount rate for the shield is the unlevered cost of capital, recompute the shield, and express it as a fraction of your answer to (a).

(c) Compute the after-tax weighted average cost of capital at debt levels of 0, 2,000, 4,000 and 6,000, using $$r\_E = r\_U + (D/E)(r\_U-r\_D)(1-\tau\_c)$$ and the values of $$V\_L$$ from (a)'s formula. State what the pattern implies for the optimal capital structure in a world with taxes and nothing else.

(d) Now introduce personal taxes. Using $$G\_L = \[1-(1-\tau\_c)(1-\theta\_e)/(1-\theta\_d)]D$$, compute the gain from the 4,000 of debt for: (i) $$\theta\_e = 0.15$$, $$\theta\_d = 0.37$$; (ii) $$\theta\_e = 0.20$$, $$\theta\_d = 0.37$$; (iii) $$\theta\_e = 0.15$$, $$\theta\_d = 0$$. Comment on the sign in each case.

(e) Suppose the firm's marginal bondholder is a pension fund but its marginal shareholder is a high-bracket individual. Which row of your answer to (d) applies, and what does that imply about the relationship between a firm's optimal leverage and the composition of its investor base? Connect your answer to §23.7.

**Problem 3 — A Myers-Majluf decision.** A firm's assets in place are worth 150 if management has favorable private information and 50 if unfavorable; outsiders assign probability one half to each. A project requires an outlay of 20 and is worth 25 gross, in both states. The firm has no cash and can raise the 20 only by issuing equity.

(a) Compute the pooled post-issue firm value and the fraction of the firm that new shareholders must receive.

(b) For each type, compute old shareholders' stake at the pooled price, and the gain or loss relative to skipping the project. Which types issue?

(c) Show that the separating outcome — only the unfavorable type issues — is consistent: compute the fraction sold at the separating price, verify that the unfavorable type's old shareholders capture the full net present value, and verify that the favorable type would lose by deviating.

(d) The project's gross value rises to 32, holding the outlay at 20. Redo (a) and (b). At what gross project value does the favorable type become willing to issue at the pooled price? Interpret the threshold.

(e) Return to the original numbers and suppose the firm can instead issue riskless debt of 20. Show that both types take the project. Then suppose the debt is risky, worth 20 if the assets are good and 16 if bad. Show why the ordering of §23.3 is a ranking of information sensitivity rather than a ranking of securities as such.

**Problem 4 — A payout tax clientele.** A firm has 1,000 shares outstanding trading at 50, of which 5,000 of value is cash it intends to distribute. Dividends and realized long-term capital gains are both taxed at 23.8 percent. Consider three holders of 100 shares each: A, taxable with a cost basis of 30 per share, who will sell pro rata into any repurchase; B, taxable with the same basis, who will not sell; and C, a tax-exempt pension fund.

(a) Compute the dividend per share and the ex-dividend price, and the number of shares repurchased and the post-repurchase price, under the two alternatives.

(b) Compute each holder's after-tax wealth under each alternative and the difference. Show that A's advantage from the repurchase equals the tax rate times the basis returned.

(c) Holder B pays no tax now. Is the repurchase therefore free for B? State precisely what has and has not happened to B's tax liability, and what determines the value of the difference.

(d) The firm's shareholder register is 70 percent tax-exempt. Compute the value-weighted advantage of a repurchase over a dividend for the whole register, assuming the remaining 30 percent is split evenly between A-types and B-types. Comment on what this implies about the payout policy of a firm held mostly by pensions.

(e) Suppose instead that dividends are taxed at 40.8 percent and capital gains at 23.8 percent. Compute the ex-day price drop per dollar of dividend implied by the marginal holder's rates, and state two reasons why an econometrician should not read an estimated ex-day ratio as that holder's tax rate.

**Problem 5 — Gap-filling reasoning.** The Treasury announces a shift in its issuance toward longer maturities, raising the share of its outstanding debt with more than ten years remaining by five percentage points over two years. Nothing else about the fiscal position changes.

(a) Using the preferred-habitat framework of Chapter 9 §9.5, state what happens to the term premium at long maturities and why.

(b) State the gap-filling prediction for corporate issuance, and explain the mechanism in terms of the *relative* price of long and short corporate claims.

(c) Which firms should respond, and which should not? Give two firm characteristics that should predict responsiveness, and explain each in terms of the cost of exercising the maturity choice.

(d) Greenwood, Hanson and Stein report that corporate maturity choice predicts excess returns on long bonds. Explain why this follows from the mechanism rather than being an additional assumption, and state what it would mean if the prediction failed.

(e) Now design the objection. A skeptic argues the correlation is spurious: the government lengthens in the same conditions that make firms want to shorten for unrelated reasons — a recession, say, in which firms are reluctant to lock in long-term obligations. Construct the strongest version of this objection and describe the identification strategy that would answer it.

**Problem 6 — Reading a capital structure.** A mature manufacturer has 8,000 of equity at market value, 2,000 of debt, an operating margin well above its industry median, tangible assets that are 70 percent of its book total, and no research and development spending. Over the last decade its share price has roughly tripled and it has issued no equity.

(a) State what each of the three theories predicts about this firm's leverage relative to its industry, and identify where they disagree.

(b) The firm's leverage is 20 percent against an industry median of 40 percent. Which theory does the observation favor, and what is the alternative explanation from each of the other two?

(c) The firm announces a large debt-financed repurchase, taking leverage to 40 percent. Give the trade-off, free-cash-flow, and signaling interpretations of the announcement, and state what each predicts for the announcement return and for subsequent investment.

(d) An analyst values the tax shield at $$\tau\_c$$ times the new debt and adds it to the equity value. Give two reasons the number is too high and one reason it could be too low.

(e) The firm's bonds are bought overwhelmingly by insurers. Using §23.7 and Chapter 10 §10.9, explain how this fact bears on both the spread the firm pays and the amount it chooses to borrow.

***

## Selected Solutions

*Solutions to Problems 1 and 4 follow. Solutions to the remainder are in the instructor materials.*

**Problem 1.**

(a) Under Proposition I, $$V\_L = V\_U = 10{,}000$$, so L's equity is worth $$10{,}000-4{,}000 = 6{,}000$$. Interest is $$0.05\times 4{,}000 = 200$$, leaving $$1{,}000-200 = 800$$ for equity, a cost of equity of $$800/6{,}000 = 13.33$$ percent. Proposition II gives $$0.10 + (4{,}000/6{,}000)(0.10-0.05) = 0.10+0.0333 = 13.33$$ percent. The weighted average is $$0.6\times 13.33 + 0.4\times 5 = 8.0 + 2.0 = 10$$ percent, equal to $$r\_U$$ and therefore to U's cost of capital.

(b) Put up 6,000, borrow 4,000 at 5 percent, and buy 10,000 of U. The payoff is $$1{,}000 - 0.05\times 4{,}000 = 800$$ on 6,000 of own capital, a return of 13.33 percent — identical to L's equity in level and in risk, since the borrowing is riskless and the residual variability is entirely U's operating cash flow scaled by $$10{,}000/6{,}000$$.

(c) Buy one percent of L's debt as well as one percent of its equity: cost $$0.01\times 6{,}000 + 0.01\times 4{,}000 = 100$$, payoff $$0.01\times 800 + 0.01\times 200 = 10$$. That is one percent of U, at one percent of U's price. Holding both sides of a levered firm's capital structure is holding the unlevered firm — which is the same statement as Proposition I.

(d) Sell short one percent of L's equity, receiving $$0.01\times 6{,}500 = 65$$; borrow $$0.01\times 4{,}000 = 40$$ at 5 percent; buy one percent of U for 100. Net cash today $$65+40-100 = +5$$. In every subsequent year: receive $$0.01\times 1{,}000 = 10$$ from U, pay $$0.01\times 800 = 8$$ on the shorted equity, pay $$0.01\times 200 = 2$$ of interest — net zero, in every state, forever. The trade is money for nothing and scales linearly, so at full size it yields 500. Arbitrageurs shorting L's equity and buying U push $$V\_L$$ down and $$V\_U$$ up until the two meet.

(e) Many possible answers. **A short-sale constraint or a prohibition on shorting** removes the trade entirely and leaves $$V\_L$$ free to exceed $$V\_U$$, since only the correcting direction is blocked — this is Chapter 15 §15.5's asymmetry, applied to a capital structure. **A leverage constraint** — a mandate forbidding borrowing, as at most pension plans and long-only funds — prevents the investor in (b) from manufacturing homemade leverage, which makes a levered firm a *service* to constrained holders and again pushes $$V\_L$$ above $$V\_U$$; this is Chapter 4 §4.9's betting-against-beta logic transposed to the issuing side. Both frictions point the same way, which is worth noticing: the observed direction of the failure of irrelevance is not symmetric.

**Problem 4.**

(a) The dividend is $$5{,}000/1{,}000 = 5$$ per share and the ex-dividend price is $$50-5 = 45$$. The repurchase retires $$5{,}000/50 = 100$$ shares, leaving 900 shares against $$50{,}000-5{,}000 = 45{,}000$$ of value, a price of $$45{,}000/900 = 50$$ — unchanged, which is the point.

(b) **A** under a dividend: 100 shares at 45 is 4,500, plus $$100\times 5\times(1-0.238) = 381$$ of after-tax cash, for 4,881. Under the repurchase, A sells its pro-rata share, $$100\times(100/1{,}000) = 10$$ shares, for 500, on which the taxable gain is $$10\times(50-30) = 200$$ and the tax $$0.238\times 200 = 47.6$$; A holds 90 shares at 50 (4,500) plus $$500-47.6 = 452.4$$, for 4,952.4. The advantage is $$4{,}952.4-4{,}881 = 71.4$$, which is $$0.238\times(10\times 30) = 0.238\times 300 = 71.4$$: the tax on the returned basis, which a dividend taxes and a sale does not. **B** under the dividend: 4,881, as above. Under the repurchase B sells nothing and holds 100 shares at 50, for 5,000 — an advantage of 119.0. **C** receives $$100\times 45 + 100\times 5 = 5{,}000$$ under the dividend and holds $$100\times 50 = 5{,}000$$ under the repurchase: no difference at all.

(c) It is not free. B's basis is unchanged at 30 and its per-share market value is unchanged at 50, so the *unrealized* gain of 2,000 is intact and will be taxed on eventual sale. What B has gained is deferral, and the value of that gain is the time value of the deferred tax over B's remaining holding period — which goes to the full 119.0 if the shares are never sold and are stepped up at death (Chapter 14 §14.5), and toward zero if B sells next week.

(d) Every holder in the register receives 500 of distribution per 100 shares. The value-weighted advantage of the repurchase is $$0.70\times 0 + 0.15\times 71.4 + 0.15\times 119.0 = 10.71 + 17.85 = 28.56$$ per 100 shares, or $$28.56/500 = 5.7$$ percent of the amount distributed — against 14.3 percent for the A-types and 23.8 percent for the B-types taken alone. The implication is that for a firm held mostly by pensions the tax case for repurchases is weak, and the observed preference for repurchases at such firms must be doing other work — flexibility, per §23.5, or the reluctance to establish a commitment that a dividend would represent. Payout form is not explained by taxes alone, and knowing the register tells you how much of the explanation taxes can carry.

(e) The implied ex-day drop is $$(1-\theta\_d)/(1-\theta\_e) = (1-0.408)/(1-0.238) = 0.592/0.762 = 0.777$$ per dollar of dividend. Two reasons not to read that as anyone's tax rate. **Short-horizon traders face different rates.** A dealer or a short-term arbitrageur trading around the ex-date is taxed on short-term gains at ordinary rates, so the ratio it would enforce is close to one; the observed drop is set by whoever is marginal *on that day*, which need not be the holder marginal on other days. **Microstructure bounds the arbitrage.** Tick sizes, bid-ask spreads and transaction costs put a band around the ex-day price change inside which no trade is profitable, and the estimated ratio is sensitive to where in the band the price is measured and to which quote convention is used. A third, if wanted: risk. Holding a share across the ex-date is not riskless, so an arbitrage argument pinning the ratio to a tax ratio requires a hedge that is itself imperfect.

***

## Data Exercise: Leverage, Payout, and a Tax Reform

Parts A through C run entirely on free data. Part D is the licensed extension.

**Part A — Corporate leverage over sixty years (free, FRED and Z.1).** The Financial Accounts of the United States report the balance sheet of the nonfinancial corporate business sector quarterly, including debt outstanding, the market value of equity, and net worth at both historical and current-cost valuation. Work from the Z.1 balance-sheet table for the sector rather than from remembered FRED mnemonics, which have changed across vintages, and confirm from the table's own notes which valuation basis each line uses.

1. Construct two leverage series from the earliest available date: debt over net worth at current cost, and debt over the sum of debt and the market value of equity. Plot both. Explain in three sentences why they can move in opposite directions over a decade, and which one a trade-off theory is a statement about.
2. Mark 1974, 1982, 1989, 2000, 2009, 2020, and the most recent observation. For each, state in one line whether the move in the market-value series came from the numerator or the denominator.
3. Compute the standard deviation of annual changes in each series and the first-order autocorrelation of the levels. Relate what you find to §23.2's persistence and slow-mean-reversion facts, and say honestly what an aggregate series can and cannot establish about firm-level targets.

**Part B — Dividends against buybacks (free, Z.1 and NIPA).** Aggregate payout can be assembled two ways, and the two disagree, which is the exercise. The Financial Accounts report net equity issuance for the nonfinancial corporate sector (negative for most of the last four decades, per Chapter 12 §12.6), and the national accounts report net dividends paid by corporate business.

4. Plot net dividends and the negative of net equity issuance on one axis, as shares of corporate gross value added. Identify the crossover period and describe the trend in the payout mix.
5. The negative of net equity issuance is *not* the same thing as gross repurchases: it nets out issuance for employee compensation and includes equity retired in cash mergers. List every component you can identify from the Z.1 documentation, and state which direction each biases your series as a measure of buybacks. Where a component cannot be separated in free data, say so and hedge the series accordingly.
6. Compute the volatility of the dividend series and of the net-issuance series, both as shares of value added, and both in levels and in year-on-year changes. Which is smoother, by how much, and what does the comparison say about §23.5's flexibility argument?

**Part C — The 2017 reform in the data (free, BEA and Z.1).** The Tax Cuts and Jobs Act, enacted December 2017, cut the federal corporate rate from 35 to 21 percent, capped the deductibility of net interest, and moved the United States toward a territorial system with a one-time transition tax on accumulated foreign earnings. Predicted effects: lower leverage, and a wave of repatriation.

7. Retrieve the BEA's international transactions series for repatriated dividends from foreign affiliates of US multinationals. Plot the annual series from 2010 and describe the 2018 pattern. State the magnitude relative to the preceding years' average, and hedge appropriately — the series is revised and the definitions changed.
8. Overlay your Part A leverage series and your Part B payout series on the same window, 2014 to the present. Does leverage fall after 2018? Does payout rise? Report what you see and, in a paragraph, list at least three things happening simultaneously that make an aggregate before-and-after comparison uninformative about the tax channel.
9. The opening episode's firm was the canonical borrower-against-offshore-cash. Using public quarterly filings, chart one large technology firm's gross cash, gross debt, and net debt from 2012 to 2022. Identify the point at which gross debt stops rising and state what changed. This is a case study, not identification; write two sentences on what a serious identification strategy would need instead, and connect them to §23.6's discussion of staggered tax-change designs.

**Part D ★ — Firm-level tests (WRDS).** With Compustat and CRSP:

10. Build an annual panel of US nonfinancial firms and estimate a standard leverage regression on Frank and Goyal's six factors. Report coefficients, and the within- and between-$$R^2$$. Then add firm fixed effects and report what happens to the $$R^2$$ and to the profitability coefficient. Comment on Lemmon, Roberts and Zender.
11. Estimate a partial-adjustment model of leverage toward a fitted target and report the implied speed of adjustment and half-life, using at least two estimators (pooled OLS and a within estimator). Explain why the two differ and in which direction the bias runs.
12. Construct Baker and Wurgler's external-finance-weighted market-to-book ratio and regress leverage on it, controlling for the contemporaneous ratio. Report the coefficient at horizons of one, five and ten years after the weighting window. Then implement Leary and Roberts's test: simulate the leverage path a firm would follow with no rebalancing at all, and report how much of your estimated persistence the mechanical channel reproduces.
13. Merge Treasury maturity-structure data (the Treasury's monthly statement, or the CRSP Treasury file) onto aggregate corporate issuance from Mergent FISD, and estimate the gap-filling regression of the corporate long-term share on the government long-term share. Split the sample by issuer size and rating, and report whether the effect is concentrated where §23.7 says it should be. Figure 23.6 gives you the government side for free, and it is the half the published aggregates measure cleanly; what this exercise adds is the corporate side, which requires security-level issuance because netting destroys it in any aggregate. Report the gross-issuance long share you construct alongside the net-issuance version from the Financial Accounts, and state how much of the relationship the netted series loses.