第四章 资本结构与股利政策 — 知识点讲解

1. Core Idea

To grow, a firm either borrows (debt financing) or sells a piece of itself (equity financing). Equity financing follows a life-cycle ladder: private early-stage financing (venture capital / private equity for nonpublic firms) → IPO (initial public offering, an unseasoned new issue) — the firm's first public sale of stock → SEO (seasoned equity offering) — a new issue by a firm with outstanding securities. There are two selling routes: a public issue must be registered with the SEC; a private issue to fewer than 35 investors requires no registration. On December 11, 2019, Saudi Aramco offered 3 billion shares (1.5 percent of the firm) at 32 riyals ($8.53) per share, raising $25.6 billion and reaching a $1.88 trillion valuation — the largest IPO in history. That is what this chapter studies.

2. Early-Stage Financing and Venture Capital (15.1)

Venture capital (VC) means financing for new, often high-risk ventures. Angels invest their own money in smaller deals; VC firms pool funds from individuals, pension funds, insurance companies, large corporations, and university endowments; private equity is the broad term for equity financing of nonpublic companies. VC money is provided in stages, each round sized to reach the next milestone:

Facts: in 2019 only $9.6 billion went to angel/seed rounds vs. $80.7 billion to later VC and $66.4 billion to growth equity — the dollar volume is in late stages; only 1 of every 100 proposals is funded; VCs typically demand 40 percent or more of the equity, voting preferred stock, and board seats. Crowdfunding: under the JOBS Act (2012), the cap rose from $1 million to a $50 million maximum per 12-month period; Regulation CF (May 2016) admits non-accredited investors ("accredited" = $1 million+ net worth or $200,000+ income in two of the past three years).

3. The Basic Procedure of Going Public (15.2–15.3)

Regulatory framework: the Securities Act of 1933 governs new interstate issues, the Securities Exchange Act of 1934 governs outstanding securities, and the SEC administers both. Procedure: board approval (a shareholder vote may be needed to raise authorized shares) → file a registration statement with the SEC → 20-day waiting period (during which only the preliminary prospectus, or red herring, may be circulated and only oral offers made) → on the effective date the price is set and full-scale selling begins; tombstone ads rank underwriters into brackets. The SEC checks compliance with rules only — it does not pass on merits or verify the prospectus. Registration is waived for loans maturing within nine months and for issues under $5 million (Regulation A, brief statement).

Issue methods (Table 15.6): public issues are either general cash offers or rights offers (offered first to existing owners; rare in the U.S., common abroad); a private issue is a direct placement (purchaser generally could not resell for at least two years). An IPO is by definition a cash offer; a new issue by an already-public firm is an SEO.

4. Underwriters (15.4)

Underwriters formulate the issue method, price the securities, and sell them; several combine into a syndicate to share risk. The gross spread (underwriting discount) — the difference between the underwriters' buying price and the offering price — is their compensation. Three types of underwriting:

• Firm commitment: the issuer sells the entire issue to the underwriters, who resell it; the risk shifts to the underwriter. This dominates in the U.S. — over 95 percent of SEOs; pricing relies on road shows and bookbuilding
• Best efforts: no guarantee of proceeds; now uncommon
• Dutch auction (uniform price auction): investors bid and all winners pay one price. Rial sells 400 shares: A 100@$16, B 100@$14, C 200@$12, D 100@$12, E 200@$10 → the lowest price selling all shares is $12 (500 shares bid vs. 400 offered); allocation ratio = 400/500 = 80 percent. (The sole method used by the U.S. Treasury.)

Standard clauses: the Green Shoe (overallotment option) lets underwriters buy 15 percent more shares at the offering price for 30 days — they initially sell 115 percent, exercising the option if demand is strong or covering short in the market if weak; lockup agreements bar insiders from selling for 180 days after the IPO (not legally required); the quiet period ends 40 calendar days after the IPO, during which analysts cannot issue recommendations; direct listings bypass underwriters entirely (Slack, June 2019, ~$12 billion valuation) and save all underwriting fees.

5. IPO Underpricing (15.5)

Underpricing — pricing below true value — is common; it is an indirect cost borne by existing shareholders. Vroom (2020): offered at $22, closed day one at $47.90 — $25.90 per share, about $550 million left on the table on 21.25 million shares. Long-run evidence (Table 15.7; first-day return = offering price to first closing price):

Partial adjustment phenomenon: 1980–2019, 49 percent of IPOs priced within the file range, 28 percent below, 23 percent above; issues priced above the range were underpriced by 50 percent on average vs. 3 percent for those below (122% vs. 8% in 1999–2000) — offers are raised only partially, and underpricing is worst when the price is pushed above the range. Why underpricing persists (four explanations): ① young firms with little or no sales must be underpriced to attract investors; ② the winner's curse — the average investor gets full allocation mainly in issues smart money avoids, so underwriters must underprice on average to keep him in the game; ③ insurance against lawsuits by customers; ④ compensation to institutions that truthfully reveal demand in bookbuilding. Chinese IPOs averaged a 157.7 percent first-day return (1990–2017) vs. 16.8 percent in the U.S.

6. Seasoned Offerings and Firm Value (15.6)

Intuition says good projects should raise the stock price; the evidence says otherwise: prices fall on announcement of a new equity issue — about 3 percent on average for industrial firms — the abnormal return, an indirect flotation cost. Shopify fell about 5 percent (Sept. 2019); Roku dropped 7 percent on announcement day (Dec. 2019). Three explanations: ① managerial information — management issues when shares are overvalued, and new shareholders discount the price accordingly; ② debt usage signal — if projects were great, why let new shareholders in? Issuing equity reveals too much debt or too little liquidity; ③ issue costs. Debt announcements do not fall — evidence that positive-NPV projects should be debt-financed.

7. The Costs of Issuing Securities (15.7)

Flotation costs have six components: gross spread, other direct expenses, indirect expenses, abnormal returns, underpricing, and the Green Shoe. Evidence: a small IPO (under $10 million) carries direct costs of 25.22 percent of the amount raised (a $10 million issue nets only about $7.5 million); issues over $500 million cost 5.5 percent; the spread is exactly 7 percent for over half of all IPOs. Patterns: ① substantial economies of scale; ② debt is far cheaper than equity (investment-grade straight bonds under $10 million cost 1.90% vs. 5.27% junk; over $500 million only 0.08%); ③ IPOs cost more than SEOs, but not by much; ④ straight bonds beat convertibles. Overall, direct costs run about 10 percent of proceeds and underpricing about 19 percent. Case: Black Diamond (Jan. 30, 2020) sold 10,586,316 shares at $19, grossing $201.1 million; after the 7 percent spread it kept $184.4 million, total direct expenses $16.77 million = 8.97 percent of proceeds; the stock closed day one at $39.48 (more than doubled — the indirect cost was much larger). Planning formula: to net $X with direct-cost fraction f, raise $X/(1−f) — the L5 Corporation needing $15 million net at f = 7% must raise $15m/0.93 = $16.129 million, paying $1.129 million.

8. Rights Offerings (15.8)

In a rights offering (privileged subscription), new shares are sold first to existing shareholders (mandatory if the charter has a preemptive right). National Power: 1,000,000 shares at $20, raising $5 million at a subscription price of $10:

$$\text{New shares} = \frac{\text{Funds}}{\text{Subscription price}} = \frac{\$5{,}000{,}000}{\$10} = 500{,}000; \qquad \text{Rights per new share} = \frac{\text{Old shares}}{\text{New shares}} = \frac{1{,}000{,}000}{500{,}000} = 2$$

Ex-rights price and right value (after the offer: 1.5 million shares worth $25 million): $25m/1.5m = $16.67 per share; value of a right = $20 − $16.67 = $3.33. General formulas ($N$ rights needed per new share):

$$\text{Ex-rights price } P_X = \frac{N \cdot P_{RO} + P_S}{N+1}, \qquad \text{Value of a right} = P_{RO} - P_X = \frac{P_{RO} - P_S}{N+1}$$

Check: at a subscription price of $8, National Power sells 625,000 shares, 1.6 rights each; ex-rights price $25/1.625 = $15.38; right worth $4.62 = ($20−$8)/(1.6+1) ✓. Lagrange Point ($40 stock, one new share per five owned at $25): ex-rights price (5×$40+$25)/6 = $37.50; right = $2.50; if rights trade at $2, buying five rights ($10) plus $25 buys a $37.50 share — $2.50 arbitrage per share. Key conclusions: shareholders neither gain nor lose whether they exercise or sell; the ex-rights price drop (ex date = one trading day before the record date) is like a stock split; the subscription price is arbitrary as long as it is below the market price and nonzero — a rights offer cannot be underpriced; rights offers are cheaper than cash offers (no underwriter needed) but rare in the U.S.; standby underwriting (a firm commitment on the unsubscribed portion) plus an oversubscription privilege protects against undersubscription. Hadron (3m shares at $40, raising $20m at $25): 800,000 new shares; ex-rights price $140m/3.8m = $36.84; right = $3.16.

9. Dilution (15.9)

Dilution is a loss in existing shareholders' value, of three kinds: ① dilution of percentage ownership — Joe's 5,000/50,000 shares (10 percent) fall to 5,000/100,000 (5 percent) after 50,000 new shares are sold (a rights offer avoids this); ② dilution of market value; ③ dilution of book value and EPS. A common misconception: issuing shares with a market-to-book ratio below 1 always cuts EPS (accounting dilution is indeed unavoidable), but market value dilution need not occur. USM: 1 million shares at $5 (market value $5m), book value $10m, NI $1m, EPS $1, ROE 10%, P/E 5, M/B = .5; the new plant costs $2m, financed by 400,000 new shares at $5:

The truth: the price falls because the project's NPV is negative (value rises only $1m, a $0.71 loss per share), not because M/B < 1; with NPV = +$1m, market value rises $3m and the price rises to $5.71 — accounting dilution still occurs but has no economic consequence. Book dilution is irrelevant; market dilution depends on the sign of the project's NPV.

10. Key Takeaways

1. One growth ladder — angel round → VC rounds → bridge financing → IPO → SEO; the private market (VC/private equity/direct placement) is essential for nonpublic firms, and the dollar volume concentrates in late stages.
2. The IPO toolbox — underwriting (firm commitment dominates; Green Shoe 15%/30 days; lockup 180 days; quiet period 40 days), underpricing (17.3 percent long-run average; worst when priced above the file range), and costs (25.22 percent direct for small issues; 7 percent is the modal spread); the abnormal return — about −3 percent on SEO announcements — is the key indirect cost.
3. Rights and dilution — the right is worth (P_RO − P_S)/(N+1); shareholders are unharmed and the subscription price is arbitrary; issuing equity dilutes ownership and book values, but true market-value dilution comes only from negative-NPV projects.

1. Core Idea

A firm raises capital by borrowing (debt financing) or by selling ownership (equity financing). Debt is a promise: to make regularly scheduled interest payments and to repay the principal. A firm's credit rating determines how cheaply and how easily it can borrow. This note covers three pieces of the debt puzzle: what a bond looks like (§7.2 features and covenants), how debt is sold (§15.10 public vs. private), and how ratings price the debt (§7.3 rating system plus §15.7 flotation-cost data). One fact frames everything: more than 50 percent of all debt is issued privately—the public market is not the main channel for debt financing.

2. Bond Features: The Basics (§7.2)

Three fundamental differences between debt and equity:

Terminology: the debtor/borrower is the corporation; the creditor/lender provides the funds. A creditor's maximum reward is capped by the amount of the loan, while equity rewards have no upper limit. Debt with maturity of one year or less is short-term (unfunded) debt; longer maturities are long-term. An original maturity of 10 years or less makes the instrument a "note"; longer issues are "bonds"—original maturity is the only formal distinction.

The indenture is the written agreement between the corporation (borrower) and its creditors (a.k.a. deed of trust), often several hundred pages. A trustee (usually a bank) represents bondholders: (1) ensures the indenture's terms are obeyed, (2) manages the sinking fund, (3) represents bondholders in default. Six standard provisions: basic terms, total amount issued, property used as security, repayment arrangements, call provisions, protective covenants.

Security and seniority: - Mortgage securities are secured by real property (land, buildings); a blanket mortgage pledges all real property; collateral trust bonds pledge securities such as stock. - A debenture is an unsecured bond—holders claim only property not otherwise pledged; unsecured issues with maturity under 10 years are called notes. - Seniority: holders of subordinated debt are paid only after specified creditors are compensated; debt can never be subordinated to equity.

Repayment and calls: - Sinking fund: an account managed by the trustee for repaying bonds—annual payments retire a fraction of the issue by buying bonds in the market or calling a fraction; may start about 10 years out and may leave a "balloon payment" at maturity. - Call provision: the company repurchases bonds at stated prices; call premium = call price − stated value, often initially equal to one annual coupon and declining to zero; a deferred call (e.g., no calls for the first 10 years) makes the bond call-protected. - Make-whole call: bondholders receive approximately what the bonds are worth—the present value of remaining interest and principal discounted at an indenture-specified rate (Apple: "Treasury rate plus .20%"). The lower interest rates, the higher the make-whole call price.

Protective covenants: negative ("thou shalt not": limit dividends by formula, pledge no assets to other lenders, no mergers, no major asset sales/leases, no additional long-term debt) and positive ("thou shalt": maintain minimum working capital, furnish audited financial statements, keep collateral in good condition).

Apple bond example (issued 9/11/2019, matures 9/11/2049): face value $2,000; annual coupon 2.95% = $59 per year ($29.50 on 3/11 and 9/11); offer price 99.270% of face = $1,985.40 per bond; unsecured, no sinking fund, make-whole call; rated Moody's Aa1 / S&P AA+.

3. Issuing Debt: Public versus Private (§15.10)

The procedure parallels equity (SEC registration, prospectus), except the bond registration statement must include the indenture. The two forms of direct private long-term financing: - Term loans: direct business loans with maturities of one to five years, mostly repaid during the life of the loan; lenders include commercial banks and insurance companies. - Private placements: like term loans but with longer maturities.

Five differences from public debt: ① a direct loan avoids SEC registration costs; ② direct placement typically has more restrictive covenants; ③ a term loan or private placement is easier to renegotiate in default (a public issue has hundreds of holders); ④ life insurance companies and pension funds dominate private placements, commercial banks the term-loan market; ⑤ distribution costs are lower in the private market. The price: interest rates on private debt are usually higher than on an equivalent public issue—the trade-off between a higher rate and more flexible distress arrangements plus lower issue costs. Overall: flotation costs are far lower for debt than for equity (Section 5).

4. Credit Ratings (§7.3)

The two leading agencies, Moody's and S&P, rate debt as an assessment of the issuer's creditworthiness: the likelihood of default and the protection creditors have in default. Crucially, ratings address only default risk, not interest rate risk—a highly rated bond's price can still be volatile.

Investment grade = BBB or better (S&P), Baa or better (Moody's); anything below is noninvestment grade, or junk. Key facts: - AAA is almost never awarded: as of February 2020, only Johnson & Johnson and Microsoft among U.S. nonfinancial companies held AAA. - Split ratings ("crossover" or "5B" bonds): rated triple-B/Baa by one agency and double-B/Ba by the other. - Fallen angels: investment-grade bonds cut into junk territory. Example: S&P cut Kraft Heinz from BBB− to BB+ in February 2020; by May 2020 there were 24 U.S. fallen angels affecting more than $300 billion in debt, with another 111 companies ($444 billion) at risk of falling. - Notches: S&P uses plus/minus (A+ strongest A rating, A− weakest); Moody's uses 1, 2, or 3 (1 highest).

Ratings and default rates (S&P Global cumulative defaults, 1981–2019)—ratings matter because defaults really do occur: - About 30 percent of CCC/C-rated bonds default within one year, ~50 percent within nine years; - Only about 1–2 percent of AAA- and AA-rated bonds default within 20 years; - After 10 years the default rate for BB bonds is more than twice that for BBB bonds—the investment-grade cutoff is a real, dollar-denominated line.

5. Ratings Drive Issue Costs (§15.7 data)

Debt offerings exhibit substantial economies of scale, and investment-grade issues have much lower direct costs than junk (straight bonds, excluding convertibles):

For contrast, equity: total direct costs of an IPO average about 10 percent of proceeds; the typical underwriting spread is exactly 7 percent for well over half of IPOs; in the S&S Air minicase the same underwriter charged 4 percent on the bond offering (7 percent on the IPO). Bottom line: debt is much cheaper to float than equity, and higher-rated debt is much cheaper than junk—which is why weak credits pay up in interest for private, flexible funding.

6. Key Takeaways

1. Three faces of debt — indenture terms (security, calls, covenants) determine what the bond looks like; public vs. private determines how it is sold; the credit rating determines what it costs.
2. Private issuance is the norm — more than 50 percent of debt is privately placed: no SEC registration costs, renegotiable in distress, cheaper distribution—paid for with higher rates and tighter covenants.
3. Ratings measure default risk only — a high rating does not mean stable prices; the default-rate chasm across the investment-grade line (BB defaults more than twice as often as BBB over 10 years) maps directly into issue costs (1.90% vs. 5.27%).

1. Core Idea

M&M Proposition I (no taxes): In a perfect market with no taxes and no bankruptcy costs, the value of the firm is completely independent of its capital structure—the value of the levered firm equals the value of the unlevered firm:

$$V_L = V_U$$

The pie model: View the firm as a pie; the equity slice E and the debt slice D (e.g., 40%–60% versus 60%–40%) are merely two ways of cutting it. The size of the pie does not depend on how it is sliced, because the assets on the left-hand side of the balance sheet are identical. As Miller put it: cut a pizza into eighths and you have more pieces, but not more pizza. Corollary: the weighted average cost of capital (WACC) is the same regardless of the debt-equity ratio—cheap debt is exactly offset by the higher equity risk that leverage creates.

2. The Effect of Financial Leverage: Trans Am (Tables 16.3-16.4)

Trans Am has assets worth $8,000,000, 400,000 shares outstanding at $20, and no debt. Proposal: borrow $4,000,000 at 10 percent and repurchase $4M/$20 = 200,000 shares, leaving 200,000; D/E goes from 0 to 1. With no taxes, three EBIT scenarios:

Leverage magnifies the dispersion of shareholder returns: EPS rises to $5.50 in the good state and falls to $0.50 in the bad state. EPS is twice as sensitive to EBIT under leverage (each $400,000 of EBIT moves EPS by $2 versus $1). Leverage creates no value; it only reallocates payoffs and risk.

3. Break-Even (Indifference) EBIT

Set EPS equal across structures: $EBIT/400{,}000 = (EBIT - \$400{,}000)/200{,}000$, which gives EBIT = $800,000, where EPS = $2 under either structure. Intuition: at EBIT of $800K the all-equity ROE is $800K/$8M = 10 percent—exactly the interest rate—so the firm's earnings just cover its interest. Above this point leverage helps; below it, it hurts. Example 16.1 (MPD): $1,000,000 of debt at 9 percent, 200,000 shares at $20, 50,000 repurchased leaving 150,000, interest $90,000. Solving $EBIT/200{,}000 = (EBIT - \$90{,}000)/150{,}000$ gives break-even EBIT = $360,000 (EPS = $1.80 in both)—the minimum EBIT management must expect for the restructuring to raise EPS.

4. Homemade Leverage: The Logical Foundation

Key point: conclusion 4 (capital structure matters) does not follow, because shareholders can duplicate or undo any corporate leverage on their own—personal borrowing that changes financial leverage is homemade leverage.

Identical net cost and identical payoffs in every state—the proposed structure merely does for shareholders what they could do for themselves. Unlevering (Example 16.2): if the firm adopts debt but an investor prefers the all-equity structure, sell 50 shares for $1,000 and lend at 10 percent: 50 × EPS ($0.50/$3.00/$5.50) = $25/$150/$275 plus $100 interest = $125/$250/$375—exactly the original payoffs on 100 shares ($1.25/$2.50/$3.75 × 100). Hence the stock price is the same no matter which structure Trans Am chooses.

5. M&M Proposition II (no taxes): The Cost of Equity

Changing the capital structure changes the split between E and D, not total value. With no taxes, the WACC equals the required return on the firm's overall assets, $R_A$:

$$R_A = (E/V)R_E + (D/V)R_D, \qquad V = E + D$$

Rearranging for the cost of equity gives M&M Proposition II:

$$R_E = R_A + (R_A - R_D) \times \frac{D}{E}$$

The cost of equity depends on three things: $R_A$, the cost of debt $R_D$, and the debt-equity ratio $D/E$. Example 16.3 (Ricardo): $R_A$ = 12%, $R_D$ = 8%: - 80% equity, 20% debt: D/E = .25, $R_E = .12 + (.12 - .08) \times .25 = .13$ (13%), WACC = $.80 \times .13 + .20 \times .08 = .12$ - 50% equity, 50% debt: D/E = 1.0, $R_E = .12 + (.12 - .08) \times 1.0 = .16$ (16%), WACC = $.50 \times .16 + .50 \times .08 = .12$

Both WACCs are 12 percent: the greater weight on cheap debt at D/E = 1 is exactly offset by the higher cost of equity. In Figure 16.3, $R_E$ is a straight line with slope $(R_A - R_D)$, while the WACC is a horizontal line—another statement of Proposition I.

6. Business Risk and Financial Risk

Proposition II decomposes the cost of equity into two components:

$$R_E = \underbrace{R_A}{\text{business risk}} + \underbrace{(R_A - R_D) \times (D/E)}{\text{financial risk}}$$

• Business risk: inherent in the firm's operations; it depends on the systematic risk of the assets and determines $R_A$—unaffected by capital structure.
• Financial risk: $(R_A - R_D) \times (D/E)$, entirely determined by financial policy; debt financing shifts extra risk onto shareholders.
• Total systematic risk of equity = business risk + financial risk. As leverage rises, financial risk rises while business risk stays constant, so $R_E$ rises.

7. The Assumptions Behind Irrelevance

Proposition I holds only under strict assumptions—no taxes, no bankruptcy costs, no transaction costs, perfect markets. Miller's milk analogy: the farmer can sell the cream (low-yield, high-priced debt) and the skim milk (levered equity), but with no separation costs cream plus skim milk sells for exactly what the whole milk would bring. Once corporate taxes are introduced, the proposition becomes $V_L = V_U + T_C \times D$ and capital structure matters. The no-tax proposition's real value is as a benchmark: it isolates the sources of any "leverage premium" (taxes, distress costs, information asymmetry) instead of attributing it to debt itself.

8. Key Takeaways

1. The slicing is irrelevant — $V_L = V_U$: the size of the pie does not depend on how it is cut; firm value is set by the assets (the left side), not the financing mix (the right side).
2. Homemade leverage — shareholders can borrow or lend personally to replicate any capital structure; a firm cannot do anything shareholders cannot do for themselves, so the structure cannot affect the stock price.
3. The WACC is constant — $R_E$ rises linearly with D/E, exactly offsetting the weight effect of cheap debt; Proposition II is the cost-side statement of Proposition I.
4. Risk decomposition — equity risk = business risk (fixed) + financial risk (rising in D/E); leverage magnifies EPS dispersion but creates no value.
5. The assumptions are the exam point — no taxes, no bankruptcy costs; with taxes, $V_L = V_U + T_C D$ and the optimal structure tends to 100 percent debt—the launch point for the static trade-off theory.

1. Core Idea

In the no-tax M&M world there are two propositions. Proposition I says capital structure is irrelevant—total firm value and the weighted average cost of capital (WACC) are unaffected by the financing mix: "the size of the pie does not depend on how it is sliced." Proposition II answers the finer question: if firm value is fixed, how does leverage change the cost of equity? The answer: leverage raises the cost of equity, and it rises just enough to cancel out the apparent benefit of cheap debt.

Together the propositions tell one story—low-cost debt seems like a bargain, but the added risk borne by shareholders raises the return they demand; the two effects offset exactly, leaving the WACC unchanged. Caveat: you must first see why capital structure is irrelevant before you can see why the cost of equity rises with leverage—the two are two sides of the same coin.

The pie model: think of the firm as a pie with two slices—debt (D) and equity (E). Two firms with identical assets (Figure 16.2) differ only in the cut: one 40%–60%, the other 60%–40%—the pie is the same size. Proposition I in another form: the cut does not change the size of the pie.

Assumptions of the no-tax M&M world: no corporate taxes; no transaction or bankruptcy costs; individuals and firms borrow at the same rate; symmetric information. Under these conditions, any corporate financing choice can be replicated personally through homemade leverage, so capital structure creates no value.

2. Derivation: From the WACC to Proposition II

Ignoring taxes, the WACC is a weighted average of debt and equity costs ($V = E + D$):

$$WACC = \frac{E}{V} \times R_E + \frac{D}{V} \times R_D$$

The WACC is the required return on the firm's overall assets, so write it as $R_A$ ($R_A$ = required return on assets = unlevered cost of capital):

$$R_A = \frac{E}{V} \times R_E + \frac{D}{V} \times R_D$$

Rearranging for $R_E$ gives M&M Proposition II (Equation 16.1):

$$R_E = R_A + (R_A - R_D) \times \frac{D}{E}$$

Check the algebra: multiply through by $E$ in $R_A \cdot (E+D) = E \cdot R_E + D \cdot R_D$ to get $R_E = R_A + (R_A - R_D) \cdot D/E$.

3. Geometry and the Three Determinants of the Cost of Equity

$R_E$ is a straight line in the debt-equity ratio $D/E$ (Figure 16.3):

• Intercept = $R_A$: at $D/E = 0$ (all-equity firm), $R_E = R_A$—equity risk equals asset risk
• Slope = $R_A - R_D$: as leverage rises, equity risk rises and the required return $R_E$ rises linearly
• The WACC is a horizontal line: it does not depend on $D/E$—another statement of Proposition I; the weighting gain from cheap debt ($R_D < R_A$) is exactly offset by the rise in $R_E$

The three determinants of the cost of equity: the required return on assets $R_A$ (driven by operations), the cost of debt $R_D$, and the debt-equity ratio $D/E$ (driven by financial policy). Caveat: do not conclude that "cheap debt lowers the overall cost of capital"—in the no-tax world this is a zero-sum game and the WACC is constant.

4. Numerical Verification: The Ricardo Corporation (Example 16.3)

Ricardo has a no-tax WACC (i.e., $R_A$) of 12 percent and borrows at $R_D$ = 8 percent.

Case 1: 80 percent equity / 20 percent debt, $D/E = .2/.8 = .25$:

$$R_E = .12 + (.12 - .08) \times .25 = .12 + .01 = 13\%$$

$$WACC = .80 \times .13 + .20 \times .08 = .104 + .016 = 12\%$$

Case 2: 50 percent equity / 50 percent debt, $D/E = 1.0$:

$$R_E = .12 + (.12 - .08) \times 1.0 = .12 + .04 = 16\%$$

$$WACC = .50 \times .16 + .50 \times .08 = .08 + .04 = 12\%$$

The WACC is 12 percent under both structures—$R_E$ rises from 13 to 16 percent, exactly canceling the benefit of a heavier debt weight. Exam point: given $R_A$, $R_D$, and $D/E$, compute $R_E$ and verify the WACC is unchanged.

5. Business Risk and Financial Risk

Proposition II splits the cost of equity into two components:

$$R_E = \underbrace{R_A}{\text{business risk}} + \underbrace{(R_A - R_D) \times \frac{D}{E}}{\text{financial risk}}$$

• Business risk: the risk inherent in the firm's operations, driven by the systematic risk of its assets (Chapter 13); it determines $R_A$ and is unaffected by capital structure
• Financial risk: the extra risk imposed on stockholders by debt financing; it is zero for an all-equity firm, and, given business risk and $R_D$, it is entirely determined by financial policy (D/E)
• Total systematic risk of the equity = business risk + financial risk; adding leverage raises financial risk while business risk stays the same

How to think about it: bondholders bear only business risk (they are paid before shareholders); shareholders bear the additional financial risk of having operating volatility magnified. Leverage does not change the firm's overall risk—it only reallocates risk between the two classes of claimholders.

6. The Magnification Effect: Trans Am's EPS–EBIT Diagram

Leverage magnifies the volatility of shareholder returns (§16.2, Table 16.4; assets $8M, all-equity 400,000 shares @ $20 vs. debt $4M at 10%, 200,000 shares after the buyback):

In the EPS–EBIT diagram (Figure 16.1): the no-debt line starts at the origin with slope $1/400{,}000$ (each $400,000 of EBIT raises EPS by $1); the levered line has twice the slope (each $400,000 raises EPS by $2) and starts at −$400{,}000/200{,}000 = −$2 when EBIT is zero (interest must be paid regardless). Leverage doubles the sensitivity of EPS to EBIT—magnifying gains and losses alike.

Break-even (indifference) EBIT: set the two EPS lines equal:

$$EBIT/400{,}000 = (EBIT - \$400{,}000)/200{,}000 \Rightarrow EBIT = \$800{,}000$$

Above $800,000 leverage is beneficial; below it, it is not. At the break-even point EPS = $2 and ROE = 10 percent = the interest rate—the firm earns exactly enough to cover the interest. Example 16.1, MPD ($1M debt at 9%, 200,000 shares, buy back 50,000): $EBIT/200{,}000 = (EBIT - \$90{,}000)/150{,}000 \Rightarrow EBIT = \$360{,}000$, with EPS = $1.80$ in either case.

7. Homemade Leverage: Why Proposition I Holds

Homemade leverage: investors can borrow (to lever up) or lend (to unlever) on their own, replicating any corporate capital structure—so the firm's choice is irrelevant (Table 16.5):

The second strategy: 200 shares × EPS ($1.25/$2.50/$3.75) gives $250/$500/$750, minus interest $2,000 × 10% = $200, leaves $50/$300/$550—identical payoffs at the same net cost of $2,000.

The reverse (Example 16.2, unlevering): suppose the firm adopts the levered structure but the investor prefers the original one—sell 50 shares for $1,000 and lend at 10 percent: 50-share earnings $25/$150/$275 plus interest $100 gives $125/$250/$375, exactly the original 100-share payoffs (× $1.25/$2.50/$3.75). Conclusion: corporate financing choices can be replicated personally, so Proposition I holds.

8. Exam Points and Common Pitfalls

1. Pitfall: confusing $R_A$ with $R_E$—with no taxes, $R_A$ = WACC = unlevered cost of capital (constant); only $R_E$ rises with leverage
2. Pitfall: applying Proposition II to the taxed world. With taxes, $R_E = R_U + (R_U - R_D)(D/E)(1 - T_C)$, and $V_L = V_U + T_C \times D$, with the WACC falling in leverage—the no-tax case is neutral; the tax case says "more debt is better" (in the extreme, 100 percent debt)
3. Memory aid: Miller's analogies—think of the firm as a pizza: "cut into more pieces, but not more pizza"; or whole milk separated into cream (debt) and skim milk (levered equity)
4. The no-tax summary (Table 16.6): ① Proposition I: $V_L = V_U$—capital structure is irrelevant and the WACC is the same whatever the financing mix; ② Proposition II: $R_E = R_A + (R_A - R_D)(D/E)$—the cost of equity rises with debt financing, and equity risk = business risk (determines $R_A$) + financial risk (determined by D/E)
5. The computation routine: back out $D/E$ from the equity weight → plug into Proposition II to get $R_E$ → verify the constant WACC via $WACC = (E/V)R_E + (D/V)R_D$

No-tax versus with-tax comparison (must-know, Table 16.6):

Note that with no taxes, $R_A$ (return on assets) = WACC = $R_U$ (unlevered cost of capital)—the three symbols are the same concept; only with taxes do they become distinct.

9. Key Takeaways

1. The formula: $R_E = R_A + (R_A - R_D) \times (D/E)$—a line with intercept $R_A$ and slope $(R_A - R_D)$; each unit increase in D/E raises the cost of equity by $(R_A - R_D)$
2. Why the WACC is constant: the cheaper cost of debt is exactly offset by the higher cost of equity—Propositions I and II are two sides of the same coin
3. A risk perspective: leverage neither creates nor destroys value; it transfers risk from the firm to shareholders—business risk depends on the assets (what business you are in), financial risk depends on financial policy (how much you borrow)

1. Core Idea

Without taxes, M&M Proposition I says capital structure is irrelevant ($V_L = V_U$). But debt has a feature we have not accounted for: interest is tax deductible. Because interest is deducted from taxable income, the firm pays less tax—the saving is called the interest tax shield. It arises only from debt, so M&M Proposition I with taxes becomes: the value of the levered firm equals the value of the unlevered firm plus the present value of the tax shield, $V_L = V_U + T_C \times D$. Key point: for every $1 of debt, firm value rises by $T_C$ (with a 21% rate, $.21 per dollar of debt); tricky point: the shield is discounted at the cost of debt $R_D$ because it is generated by interest payments and carries the same risk; exam point: with taxes alone, the optimal capital structure is 100 percent debt—this "illogical conclusion" is exactly what motivates the bankruptcy-cost analysis of §16.5.

2. The Interest Tax Shield

Firms U (unlevered) and L (levered) have identical assets and operations, with EBIT of $1,000 expected every year forever. L has issued $1,000 of perpetual bonds paying 8 percent interest; the corporate tax rate is 21 percent.

With zero depreciation, capital spending, and NWC changes, cash flow from assets = EBIT − Taxes: $790 for U versus $806.80 for L. L's cash flow is $16.80 higher only because its tax bill is $16.80 lower:

$$\text{Interest tax shield} = \text{Interest} \times T_C = \$80 \times .21 = \$16.80 \text{ per year, forever}$$

Cash flow to stockholders is $790 (U) and $726.80 (L); to bondholders, $0 and $80. Total cash flow to L exceeds U by $16.80—since taxes are a cash outflow, interest deductibility is an annual $16.80 subsidy from the government.

3. M&M Proposition I with Taxes

The debt is perpetual, so the same $16.80 shield recurs every year forever. Because the shield is generated by paying interest, it has the same risk as the debt and is discounted at the cost of debt, $R_D$ = 8 percent:

$$PV(\text{tax shield}) = \frac{\$16.80}{.08} = \$210 = T_C \times D = .21 \times \$1{,}000 \qquad \text{(Eq. 16.2)}$$

M&M Proposition I with taxes (Eq. 16.3): $V_L = V_U + T_C \times D$. With an unlevered cost of capital of $R_U$ = 10 percent:

$$V_U = \frac{\text{EBIT} \times (1 - T_C)}{R_U} = \frac{\$790}{.10} = \$7{,}900$$

$$V_L = V_U + T_C \times D = \$7{,}900 + .21 \times \$1{,}000 = \boxed{\$8{,}110}$$

In Figure 16.4, $V_L$ is a straight line with slope $T_C$ and intercept $V_U$; the vertical distance between the two lines is $T_C \times D$. Exam point: the value of the firm rises by $.21 for every $1 of debt—the NPV per dollar of debt is $.21. Under this logic, every corporation would borrow to the absolute maximum; the optimal capital structure is 100 percent debt (the "illogical conclusion").

4. Taxes, the WACC, and Proposition II

M&M Proposition II with taxes: $R_E = R_U + (R_U - R_D) \times (D/E) \times (1 - T_C)$—equity cost still rises with leverage, but the tax term $(1 - T_C)$ slows the rise. With equity worth $E = V_L - D = \$8{,}110 - \$1{,}000 = \$7{,}110$:

$$R_E = .10 + (.10 - .08) \times \frac{\$1{,}000}{\$7{,}110} \times (1 - .21) = .1022 = 10.22\%$$

$$WACC = \frac{E}{V}R_E + \frac{D}{V}R_D(1 - T_C) = \frac{\$7{,}110}{\$8{,}110} \times .1022 + \frac{\$1{,}000}{\$8{,}110} \times .08 \times (1 - .21) = .0974 = 9.74\%$$

Without debt the WACC exceeds 10 percent; with debt it falls to 9.74 percent—the firm is better off borrowing. In Figure 16.5 the aftertax cost of debt stays flat, $R_E$ rises, and the WACC declines as the debt-equity ratio grows. Table 16.6 (tax case): debt financing is highly advantageous and, in the extreme, the optimal capital structure is 100 percent debt; the WACC decreases as the firm relies more heavily on debt. Equity risk has two parts: business risk (which sets $R_U$) and financial risk (set by D/E).

5. Example 16.4: Format Co.

Format Co.: EBIT = $126.58, $T_C$ = .21, D = $500, $R_D$ = 10%, $R_U$ = 20%. All cash flows are perpetuities:

$$V_U = \frac{\text{EBIT} \times (1 - T_C)}{R_U} = \frac{\$126.58 \times .79}{.20} = \frac{\$100}{.20} = \$500$$

$$V_L = V_U + T_C \times D = \$500 + .21 \times \$500 = \$605; \qquad E = V_L - D = \$605 - \$500 = \$105$$

$$R_E = R_U + (R_U - R_D)\frac{D}{E}(1 - T_C) = .20 + (.20 - .10) \times \frac{\$500}{\$105} \times .79 = .5762 = 57.62\%$$

$$WACC = \frac{\$105}{\$605} \times .5762 + \frac{\$500}{\$605} \times .10 \times (1 - .21) = .1653 = 16.53\%$$

Exam point: the WACC (16.53%) is lower than the unlevered cost of capital (20%), so debt financing is advantageous; with only $105 of equity behind $500 of debt, equity bears all residual risk and $R_E$ soars to 57.62 percent—leverage at its extreme.

6. Conclusion and Real-World Constraints

With taxes alone, the M&M analysis implies an optimal capital structure of 100 percent debt (more debt, lower WACC, higher value). Three reasons this fails in practice:

• Bankruptcy costs (§16.5): the higher the D/E ratio, the higher the probability of default; direct costs (legal and administrative) run 1.4–3.4 percent of pre-bankruptcy value (Lehman's $5.9 billion of costs were about 2 percent of its roughly $300 billion pre-bankruptcy value), and indirect costs are even larger. They eventually offset the tax-related gains from leverage—the optimum balances the two.
• Interest deduction limits (TCJA 2017): net interest is deductible up to 30 percent of EBITDA (2018–2021), dropping to 30 percent of EBIT after 2021 (temporarily raised to 50 percent for 2019–2020 by the CARES Act); interest that cannot be deducted in a year can be carried forward—deductibility is deferred, not lost.
• Non-debt tax shields: depreciation and other deductions also shelter income; with substantial other shields, the marginal value of the debt shield falls—in practice, heavy debt users are firms with high tax rates and few intangible assets.

7. Key Takeaways

1. The tax shield is a perpetuity — the interest tax shield equals interest × tax rate ($80 × .21 = $16.80 per year), carries the same risk as the debt, is discounted at $R_D$, and has present value $T_C \times D$.
2. M&M Proposition I with taxes — $V_L = V_U + T_C \times D$ (Eq. 16.3): firm value rises linearly with debt, by $T_C$ (here $.21) per dollar borrowed.
3. Proposition II and the WACC — $R_E = R_U + (R_U - R_D)(D/E)(1 - T_C)$; the WACC falls with leverage (10%+ → 9.74% in the U/L example; 20% → 16.53% for Format), so the tax-only optimum is 100 percent debt.
4. Theory extreme, practice balanced — bankruptcy costs (§16.5) and the TCJA interest cap (30% of EBITDA/EBIT) constrain unlimited tax shields; the optimal structure balances the tax shield against the costs of financial distress.

1. Core Idea

Debt is a double-edged sword. The benefit: interest is tax-deductible, creating an interest tax shield that raises firm value. The cost: as the debt-equity ratio rises, so does the probability of default, bankruptcy, and financial distress. The trade-off theory balances the two: at low debt levels the tax shield dominates and firm value rises; at high debt levels financial distress costs overwhelm the shield and firm value falls. The optimal capital structure lies between the extremes—neither 100 percent debt nor zero debt.

Real-world anchor: in May 2020, car rental giant Hertz—with $18.8 billion of debt, $14.4 billion secured by vehicles—filed for bankruptcy as COVID-19 killed travel; JCPenney, Neiman Marcus, and J. Crew followed. Bankruptcy is not a distant abstraction.

2. Bankruptcy Costs: Direct and Indirect

In principle, a firm is bankrupt when the value of its assets equals the value of its debt: equity is then worth zero and control passes from stockholders to bondholders. In a perfect world this transfer is costless—but in reality, it is expensive to go bankrupt, expensive enough to offset the tax gains from leverage.

Direct bankruptcy costs: the legal and administrative expenses of the proceeding—a "bankruptcy tax" on the firm.

• Lehman Brothers filed in September 2008, the largest U.S. bankruptcy to date; the NY Fed's 2019 final tally: compensation and benefits $1.97 billion, professional and consulting fees $2.56 billion, other operating expenses $1.37 billion—$5.9 billion total;
• With a pre-bankruptcy value of about $300 billion, costs ran about 2 percent of value; typical bankruptcy costs range from 1.4 to 3.4 percent of pre-bankruptcy value;
• Experts estimate the rushed asset sales cost Lehman another $75 billion.

Indirect bankruptcy costs: the costs incurred by a financially distressed firm to avoid filing—management distracted from running the business, lost sales, departing employees, dropped profitable projects. Financial distress costs = direct + indirect.

• During the 2008 distress of General Motors and Chrysler, 75 percent of Americans said they would not buy a car from a bankrupt company (warranty and parts concerns), further depressing sales.
• Whether the firm eventually fails or not, the possibility of loss is created by the debt itself—and this possibility is what limits how much debt a firm will take on.

3. The Tax Shield Foundation (§16.4 Recap)

Ignoring bankruptcy costs, the tax-world conclusion is absurdly extreme. Let EBIT = $1,000 in perpetuity; Firm U is unlevered, Firm L has $1,000 of perpetual bonds at 8 percent, and the tax rate is 21 percent:

U and L have identical assets, yet L's total cash flow exceeds U's by $16.80 ($806.80 vs. $790): interest of $80 × 21% = a $16.80 annual tax shield.

M&M Proposition I with taxes: $$V_L = V_U + T_C \times D$$

• The shield is a perpetuity discounted at the cost of debt: PV = $16.80/.08 = $210 = T_C × D;
• V_U = $790/.10 = $7,900, so V_L = $7,900 + $210 = $8,110;
• The NPV per dollar of debt is $.21. With taxes alone, the optimal capital structure is 100 percent debt—an absurdity that motivates the next section.

4. The Static Trade-off Theory

The static theory of capital structure: firms borrow until the tax benefit from an extra dollar of debt exactly equals the cost of the increased probability of financial distress. "Static" because assets and operations are taken as fixed; only the debt-equity ratio varies.

Three lines (Figure 16.6, firm value V against debt D):

The optimal capital structure is the mix at D*: debt of D*/V* and equity of 1 − D*/V*. Two key gaps:

• Static value − M&M-with-taxes value = loss in value from the possibility of financial distress;
• Static value − M&M-no-taxes value = the net gain from leverage, tax shield net of distress costs.

5. Worked Numbers: From $7,900 to $8,110

Continuing Section 3, with R_U = 10 percent (unlevered cost of capital):

• V_U = EBIT × (1 − T_C) / R_U = $790/.10 = $7,900;
• V_L = V_U + T_C × D = $7,900 + .21 × $1,000 = $8,110;
• Equity value E = V_L − D = $8,110 − $1,000 = $7,110;

M&M Proposition II with taxes: $$R_E = R_U + (R_U - R_D) \times \frac{D}{E} \times (1 - T_C)$$

• R_E = .10 + (.10 − .08) × ($1,000/$7,110) × (1 − .21) = 10.22%;
• WACC = (E/V)·R_E + (D/V)·R_D·(1 − T_C) = ($7,110/$8,110)(.1022) + ($1,000/$8,110)(.08)(.79) = 9.74%, below the 10 percent unlevered cost—leverage lowers the cost of capital.

Exam pattern (Example 16.4, Format Co.): EBIT $126.58, T_C = .21, D = $500, R_U = .20. Compute V_U = $100/.20 = $500; V_L = $500 + .21 × $500 = $605; E = $105; R_E = 57.62%; WACC = 16.53% < 20%. Three steps: V_U → V_L → E and WACC.

6. The Cost-of-Capital View: U-Shaped WACC

The structure that maximizes firm value also minimizes the cost of capital (values and discount rates move in opposite directions). Figure 16.7 plots the three capital costs against the debt-equity ratio:

• Initially: aftertax debt is cheaper than equity, so WACC falls as leverage rises;
• Past a point: the cost of debt rises and financial distress costs more than offset debt's cheapness, so WACC rises;
• The minimum WACC* occurs at D*/E*—the same D* as in the value-based view.

7. The Three Cases in Full (Figure 16.8)

The optimum sits at D*, where the tax saving on one more dollar of debt is exactly balanced by the added bankruptcy cost—the essence of the static theory. Note that the static model cannot identify a precise optimal structure; it only flags the two relevant factors: taxes and financial distress.

8. Managerial Recommendations: Who Should Borrow More

Taxes: - The tax benefit matters only to firms actually paying taxes; firms with large accumulated losses gain little from the interest tax shield; - Firms with substantial other shields (e.g., depreciation) benefit less from leverage; - The higher the effective tax rate, the greater the incentive to borrow (state taxes create different effective rates). Under the 2017 TCJA, net interest deductions are capped at 30 percent of EBITDA (2018–2021), dropping to 30 percent of EBIT from 2022; the CARES Act temporarily raised the limit to 50 percent for 2019–2020. Disallowed interest carries forward.

Financial distress: - The more volatile the EBIT, the less a firm should borrow; - Distress costs depend on how easily assets can be transferred: firms with mostly tangible, salable assets can borrow more; firms built on intangibles (employee talent, growth opportunities) find debt unattractive, because such assets effectively cannot be sold.

9. Key Takeaways

1. The tax shield pushes borrowing; distress costs pull it back—the optimum is not at either extreme but at D*, where marginal tax benefit equals marginal distress cost.
2. M&M is the frictionless benchmark: with no taxes and no bankruptcy costs, capital structure is irrelevant (Case I); add taxes alone and the optimum is 100 percent debt (Case II, absurd); add bankruptcy costs and an interior optimum emerges (Case III).
3. Two actionable decision variables—taxes (tax-paying status, effective rate, other shields) and distress (EBIT volatility, asset tangibility)—matter more than computing a precise optimum.
4. The net gain from one more dollar of debt equals T_C (the shield) minus the marginal distress cost; the two balance at D*, which corresponds to the minimum WACC*.

1. Core Idea

The pecking-order theory holds that firms follow a fixed financing hierarchy: internal financing first, then debt if necessary, and new equity as a last resort. There are two drivers: (1) selling securities to raise cash is expensive, so firms avoid it whenever possible; and (2) asymmetric information—as insiders, managers know more than the public, so issuing new equity signals that the stock may be overvalued. A highly profitable firm may never need external financing at all and ends up with little or no debt. The theory is an alternative to the static (trade-off) theory.

2. The Puzzle Left by the Static Theory

The static theory has dominated thinking about capital structure, but it has shortcomings. The most obvious: many large, financially sophisticated, and highly profitable firms use little debt—the opposite of what the static theory predicts. Under the static theory, these are precisely the firms that should use the most debt, because bankruptcy risk is low and the tax shield is substantial. Why do they use so little? The pecking-order theory may be part of the answer.

• Textbook example: In late 2019, Alphabet's balance sheet showed assets of $263 billion, almost $121 billion of which was cash or marketable securities. Alphabet held so much in securities that it was once in danger of being regulated as a mutual fund.

3. Asymmetric Information: Why Firms Avoid New Equity

Suppose you are a manager who must raise external capital for a new venture:

• You believe the stock is undervalued (prospects are brighter than outsiders realize) → you definitely do not want to issue equity—why sell cheap? → you issue debt instead.
• You believe the stock is overvalued → selling at inflated prices is tempting, but here is the rub: if you sell equity, investors will realize the shares are probably overvalued, and your stock price will take a hit. Issuing equity signals "the price is too high."
• Real-world evidence: companies rarely sell new equity, and the market reacts negatively when they do.

The financing decision itself is a signal—equity issuance exposes the insider's view of valuation (adverse selection).

4. The Pecking Order

Memory aid: "internal first, debt second, equity last."

5. Three Implications of the Pecking Order

1. No target capital structure: there is no target or optimal debt-equity ratio. A firm's capital structure is determined by its need for external financing—the amount of debt simply accumulates as a by-product of past financing decisions.
2. Profitable firms use less debt: greater internal cash flow means less external financing needed, hence less debt—the pattern actually observed for many companies, and the exact opposite of the static theory's prediction.
3. Firms want financial slack: to avoid selling new equity, firms stockpile internally generated cash. This cash reserve—financial slack—gives management the ability to finance projects as they appear and to move quickly when necessary.

6. Static Theory versus Pecking-Order Theory

The two theories are complementary, not mutually exclusive. The static theory speaks to long-run goals; the pecking-order theory to the tactical issue of raising external funds. The realistic picture: firms do have long-run target capital structures, but they deviate from those targets as needed to avoid issuing new equity.

7. Observed Capital Structures (Excerpt from §16.9)

U.S. firms generally show low debt-equity ratios, with wide variation across industries (January 2020 medians, Table 16.7):

• Only industries like airlines and cable television use more debt than equity; most rely far more heavily on equity—even though these firms pay substantial taxes.
• Per $1 of equity: Duke Energy has long-term debt of $1.1667 and total debt of $1.3223, versus Pfizer's $0.5190 and $0.6583.
• Firms generally have not borrowed up to the point of exhausting tax shields, so limits on debt must exist. Tax savings, distress costs, and pecking-order logic each explain part of the pattern, but no single theory fully explains observed capital structures.

8. Key Takeaways

1. The financing hierarchy: internal financing → debt → new equity (last resort). Everything revolves around avoiding equity issuance.
2. Asymmetric information is the engine: an equity offering signals overvaluation and draws a negative market reaction; managers who believe their stock is undervalued issue debt rather than sell equity cheaply.
3. Three implications: no target capital structure; profitable firms use less debt (contrary to the static theory); firms accumulate financial slack.
4. Exam contrast: static theory sets the long-run target; pecking-order theory explains short-run financing tactics; firms have targets but deviate from them to avoid issuing new equity.

1. Core Idea

Sections 16.6–16.9 complete the capital structure theory spectrum: the static theory (an optimal structure exists), the extended pie model (claimants on firm cash flows go far beyond shareholders and bondholders), the pecking-order theory (internal funds → debt → equity), and observed capital structures (industry regularities and the "profitable firms use little debt" puzzle). The static theory predicts that large, profitable firms should borrow heavily (big tax shields, low bankruptcy risk)—yet the opposite holds: Alphabet's balance sheet at the end of 2019 showed assets of $263 billion, almost $121 billion in cash and marketable securities, and almost no debt. Two additional perspectives fill this gap: agency cost theory and market timing theory. The former argues that "debt cures agency problems but creates new ones"; the latter argues that "capital structure is not a chosen target but the cumulative outcome of past issue decisions made at different stock price levels."

2. Theoretical Coordinates: The Static Theory and Its Gap (§16.6)

Static theory: the firm borrows until the marginal tax benefit of one more dollar of debt equals the marginal increase in expected financial distress costs; firm value is then maximized (V at optimal debt D) and the WACC minimized (WACC at D/E*). Managerial implications:

• Taxes: the tax shield matters only for firms in a tax-paying position—firms with accumulated losses get little value from it; the higher the effective tax rate, the stronger the incentive to borrow;
• Financial distress: the more volatile the EBIT, the less a firm should borrow; asset transferability determines distress costs—tangible assets support debt, intangibles (talent, growth opportunities) discourage it.

What the static theory cannot explain (§16.9): U.S. firms on average carry low leverage yet pay substantial taxes—there is a limit to debt, and tax shields are far from exhausted. The pecking-order, agency cost, and market timing theories are three complementary explanations.

3. Agency Cost Theory (I): Shareholder–Manager Conflicts

With dispersed ownership, ownership and control are separated; managers (agents) and shareholders (principals) have divergent interests, contracts are incomplete, and each side maximizes its own welfare. Agency costs = monitoring costs + bonding costs + residual loss.

Typical managerial deviations: shirking, perquisite consumption, empire building (negative-NPV acquisitions). Debt is a disciplinary device: the hard obligation to pay interest and principal drains free cash flow from managerial discretion—the Jensen free cash flow hypothesis: firms with large free cash flow and few growth opportunities should use more debt to force cash back to shareholders. Implication: equity agency costs decline with leverage—more debt, less room to squander shareholders' money.

4. Agency Cost Theory (II): Shareholder–Creditor Conflicts and the Optimal Structure

Higher leverage creates the second conflict—debt agency costs:

• Asset substitution / risk shifting: equity is a call option on firm value, so shareholders favor risky projects—upside accrues to them, downside falls on creditors; the closer to default, the stronger the incentive to gamble;
• Debt overhang (Myers): with heavy debt, the gains from positive-NPV projects accrue largely to creditors, so shareholders may refuse to invest—good projects are "hung" beneath the debt;
• Claim dilution and monitoring costs: senior debt issued later dilutes existing creditors, who protect themselves with restrictive covenants and monitoring.

Optimal capital structure = the trade-off of the two agency costs: equity agency costs fall with D/E while debt agency costs rise; the intersection pins the optimal leverage. This mirrors the extended pie model (§16.7): agency costs are one more claim on the firm's cash flows. With total value V_T = E + D + G + B + ⋯ = V_M + V_N (G = government, B = bankruptcy costs; V_M marketed claims, V_N nonmarketed claims)—capital structure leaves V_T unchanged and only reallocates it; the optimal structure maximizes V_M (shareholders + creditors) by minimizing V_N (taxes + bankruptcy costs + agency costs).

5. Market Timing Theory

The logical starting point is the information asymmetry of §16.8: as insiders, managers will not issue equity when the stock is undervalued (selling cheap is a bad deal; issue debt instead); when they believe the stock is overvalued they would like to issue, but investors read an equity sale as a signal that "the price is too high"—in reality firms rarely sell new equity, and the market reacts negatively when they do.

Market timing theory (Baker & Wurgler, 2002) pushes this logic to the extreme: managers issue equity when prices are high (high market-to-book ratio) and repurchase shares or issue debt when prices are low; capital structure is just the cumulative result of past timing decisions—there is no target debt-equity ratio. Empirical identification: an external-finance-weighted average of historical market-to-book ratios negatively predicts leverage—firms that issued stock when overvalued have low leverage today—while the current M/B has little power, confirming that history, not current trade-offs, matters. Contrast with pecking order: pecking order says equity is a last resort regardless of valuation; market timing says equity is issued only when expensive. Both predict profitable firms carry little debt (ample internal funds).

6. Observed Evidence: Real-World Capital Structures (§16.9)

Table 16.7 (U.S. industry medians; debt = book value of preferred stock plus long-term debt including amounts due in one year, equity = market value of shares outstanding):

Three regularities: ① most industries rely far more on equity than debt—only airlines, eating places, and a few others use more debt than equity; ② these firms pay substantial taxes yet have not exhausted their tax shields → there is a limit to debt; ③ wide variation across industries but similarity within → asset nature and operations (EBIT volatility, asset transferability) drive capital structure. Real-world example: Duke Energy has $1.1667 of long-term debt and $1.3223 of total debt per dollar of equity; Pfizer only $.5190 and $.6583. Magnitude anchor for bankruptcy costs (§16.5): typically 1.4%–3.4% of pre-bankruptcy value—Lehman Brothers spent about $5.9 billion on a pre-bankruptcy value of about $300 billion (≈2%)—the direct reason debt has a limit.

7. Exam Checklist: Comparing the Four Theories

Exam notes: ① a target capital structure exists only under static trade-off and agency cost (intersection) views—pecking order and market timing reject it; ② the most tested contrast: static theory cannot explain "profitable firms, low leverage," while pecking order and market timing can; ③ the extended-pie identity V_T = V_M + V_N and "optimal structure minimizes V_N" appear in fill-in-blank and true/false items; ④ "debt overhang" and "asset substitution" are standard definitional questions under debt agency costs.

8. Key Takeaways

1. The static theory has a gap — tax shields plus distress costs predict heavy borrowing by profitable firms, yet Table 16.7 shows most firms are low-leverage with tax shields far from exhausted.
2. Debt is a double-edged discipline — agency cost theory: leverage lowers equity agency costs (free cash flow hypothesis) but raises debt agency costs (asset substitution, debt overhang); the optimum lies where the two curves cross.
3. Timing shapes history — market timing theory: capital structure is the accumulated outcome of past "issue high, repurchase low" decisions, with no target; evidence is the negative explanatory power of historical weighted M/B for leverage.
4. Four theories, four questions — trade-off: where is the optimum; pecking order: why do profitable firms use little debt; market timing: why is leverage historically determined; agency cost: how debt simultaneously mitigates and creates conflicts.

1. Core Idea: Dividends versus Distributions

The term dividend usually refers to cash paid out of earnings. If a payment comes from sources other than current or accumulated retained earnings, the term distribution is used—a distribution from earnings is a dividend, while a distribution from capital is a liquidating dividend. More generally, any direct payment by the corporation to shareholders is part of dividend policy. Whatever the label, a cash dividend reduces corporate cash and retained earnings (except a liquidating dividend, which may reduce paid-in capital).

Dividends are measured three ways: dividends per share, as a percentage of market price (the dividend yield), or as a percentage of net income/EPS (the dividend payout). Scale: S&P 500 companies paid about $485 billion in dividends in 2019 and global dividends were $1.4 trillion; Microsoft and Apple each paid about $14 billion, while about 15 percent of S&P 500 companies paid no dividend at all.

2. The Four Basic Types of Cash Dividends

3. Dividend Payment: A Chronology

The decision rests with the board of directors; once declared, the dividend becomes a debt of the firm that cannot easily be rescinded. Using the Figure 17.1 example ($1 per share, declared January 15, payable February 16, record date January 30):

1. Declaration date: January 15—the board passes a resolution to pay the dividend;
2. Ex-dividend date: one business day before the record date (Thursday, January 29). Buy before this date and you get the dividend (cum dividend); buy on or after it and the previous owner gets it (ex dividend);
3. Date of record: January 30—the corporation prepares its list of stockholders; mailing delays make the ex-dividend convention necessary to remove any ambiguity;
4. Date of payment: February 16—checks are mailed.

4. The Ex-Dividend Date and Price Behavior

The value of a share should fall by about the dividend amount when it goes ex—"about" because dividends are taxed, so the actual drop may be closer to the aftertax value. Example: a $10 stock with a $1 dividend and a record date of Monday, June 11 has an ex date of Friday, June 8; the price falls about $1 between Thursday's close and Friday's open.

• Example 17.1 (Divided Airlines): $2.50 per share, payable Tuesday, May 30, record date Tuesday, May 9 → ex date Monday, May 8. Cal buys 100 shares on May 2 at $150—cum dividend—and receives $2.50 × 100 = $250; the price drops about $2.50 per share overnight at the ex date.
• TransDigm (December 2019): a $32.50 special dividend on a ~$600 stock (about 5 percent); it closed at $597.78 on December 26 and opened at $568.00 on the ex date (December 27), a drop of $29.78. At a 20 percent dividend tax rate the expected drop was about $26 ($32.50 × .80)—the actual drop was larger.

5. Stock Repurchases: An Alternative to Cash Dividends

Repurchases (buybacks) are the main alternative to cash dividends; S&P 500 companies have spent more than $5.3 trillion on them since 2010. Repurchases peaked in 2007 at about 2.5 times aggregate dividends, plunged in the 2008–2009 recession, and rebounded in 2010. Three methods:

1. Open market purchases: the firm buys like any investor without revealing itself as the buyer;
2. Tender offer: a fixed number of shares at a specific price. Example: A&C Inc., with 1 million shares at $50, offers to buy back 300,000 shares at $60; if all shares are tendered, the firm buys 3 out of every 10 shares;
3. Targeted repurchase: buying from specific stockholders—e.g., P-R Co. repurchased International Biotechnology's ~10 percent stake at $48 per share (well above the ~$38 market price) without extending the offer to other shareholders.

Note: not all announced repurchases are completed—the average completion rate over 2004–2007 was only 81 percent.

6. Cash Dividends versus Repurchase: Equivalence and Taxes

Consider a firm with excess cash of $300,000, net income $49,000, and 100,000 shares outstanding (market value $1,000,000 → $10 per share; EPS = $.49; PE = $10/$.49 = 20.4):

• Option A: $3 per share extra dividend ($300,000/100,000) → share price falls to $7; a 100-share holder has $700 of stock plus $300 cash = $1,000. Earnings and shares unchanged, so EPS stays $.49 and PE falls to $7/$.49 = 14.3.
• Option B: repurchase 30,000 shares ($300,000/$10) → 70,000 shares remain at $700,000/70,000 = $10 each; EPS rises to $49,000/70,000 = $.70 and PE = $10/$.70 = 14.3. The holder can sell 30 shares to create $300 cash + $700 stock—a homemade dividend.

Without taxes or transaction costs, a cash dividend and a repurchase are essentially the same thing. In the real world the key difference is taxation: dividends are taxed whether the shareholder wants them or not, whereas a repurchase is taxed only if the shareholder (1) actually sells and (2) has a capital gain. Example: at a 28 percent bracket, $100 of dividends on 100 shares costs $28 in tax; if $100 of stock originally bought at $60 is repurchased, the capital gains tax is only .28 × $40 = $11.20.

Exam point: a repurchase raises EPS (fewer shares, same earnings) but leaves the PE ratio exactly the same as a dividend (14.3 in both cases)—the EPS increase by itself creates no value.

7. Stock Dividends and Stock Splits

A stock dividend is paid in shares, not cash—it increases the number of shares each owner holds, so each share is worth less (20 percent dividend = one new share for every five owned). A stock split is essentially the same thing expressed as a ratio (3-for-1). Both are paper transactions: no cash flows, ownership percentages and shareholder wealth unchanged.

• Small stock dividends (< 20–25 percent) are accounted for differently from large stock dividends (> 20–25 percent; e.g., First Financial's April 2019 100 percent stock dividend, a 2-for-1 split).
• Peterson Co. example (10,000 shares at $66; market value $660,000):
• 10 percent stock dividend → 11,000 shares at $60. Accounting: common stock ($1 par) rises by $1,000 → $11,000; capital surplus rises by $65 × 1,000 = $65,000 → $265,000; retained earnings fall by $66,000 → $224,000; total equity unchanged at $500,000.
• 2-for-1 split → 20,000 shares, par halved to $.50; the three account figures are completely unchanged ($10,000 / $200,000 / $290,000)—unlike a stock dividend, a split does not reclassify retained earnings.
• 100 percent stock dividend → 20,000 shares; common stock +$10,000 → $20,000; retained earnings −$10,000 → $280,000.
• Wealth invariance: after the 10 percent dividend, 100 shares at $66 ($6,600) become 110 shares at $60 ($6,600); after the split, $660,000/20,000 = $33 per share (double the shares, half the price).
• Reverse splits: e.g., 1-for-5 or 1-for-20 (Citigroup's 1-for-10 in March 2011 cut shares from 29 billion to 2.9 billion). Cited reasons: lower transaction costs, better liquidity, "respectability," and exchange minimum-price rules (Nasdaq starts delisting when a stock trades below $1 for 30 days).
• Popular trading range argument: Microsoft has split nine times since 1986 (two 3-for-2 and seven 2-for-1 splits—one share became 288). Counterevidence: institutions account for about 90 percent of NYSE volume, and Berkshire Hathaway traded at about $345,000 per share with no problem.

8. Key Takeaways

1. Terminology: dividends are paid from earnings; distributions from other sources; liquidating dividends from capital. Cash dividends reduce cash and retained earnings.
2. The four dates: declaration → ex (one business day before record) → record → payment; the price drops by about the dividend (closer to its aftertax value). Divided Airlines: record Tuesday 5/9 → ex Monday 5/8.
3. Dividend ≡ repurchase without imperfections (same PE of 14.3; EPS $.49 → $.70); the tax advantage of repurchases ($28 vs. $11.20) favors buybacks in practice.
4. Stock dividends/splits don't create value: a small stock dividend transfers the market value from retained earnings into common stock and capital surplus (Peterson: $1,000 / $65,000 / $66,000); a split only halves par value and doubles share count.
5. Problem templates: ex price ≈ cum price − dividend (or its aftertax value); price after a stock dividend = old price ÷ (1 + percentage); price after a split = old price ÷ split ratio.

1. Core Idea

The MM dividend irrelevance proposition (Miller & Modigliani, 1961, "Dividend Policy, Growth, and the Valuation of Shares") states that in a perfect capital market, dividend policy does not affect firm value. Distinguish two concepts:

• Dividends matter — the value of a share is ultimately determined by the dividends that will be paid (the dividend discount model of Chapter 6).
• Dividend policy is irrelevant — dividend policy is merely the time pattern of dividend payout: more now versus more later. As long as the investment policy is fixed, firm value depends only on earning power and investment decisions, not on how earnings are split between dividends and retained earnings.

The dividend policy question: should the firm pay out cash to shareholders now, or invest the cash and pay it out later? The MM answer: with no taxes and no transaction costs, it makes no difference how the pie is sliced.

2. Assumptions (Perfect Capital Markets)

Corollary: dividends are the residual after all positive-NPV investments are funded—the same cake, cut differently.

3. Illustration: Wharton Corporation—Current Policy (Dividends Equal to Cash Flow)

Wharton is an all-equity firm that will dissolve in two years, generating $10,000 of cash flow per year (including liquidation proceeds), with 100 shares outstanding and a dividend of $100 per share. Required return 10%:

$$P_0 = \frac{D_1}{(1+R)^1} + \frac{D_2}{(1+R)^2} = \frac{\$100}{1.10} + \frac{\$100}{1.10^2} = \$90.91 + \$82.64 = \boxed{\$173.55}$$

The firm as a whole is worth $100 \times \$173.55 = \boxed{\$17{,}355}$.

4. Illustration: Alternative Policy (Initial Dividend Greater than Cash Flow)

Suppose the firm pays $110 per share at Date 1 ($11,000 total). Since cash flow is only $10,000, it must raise $1,000 by issuing new stock at Date 1. New stockholders require a 10 percent return, so they demand $1{,}000 \times 1.10 = \$1{,}100$ of Date 2 cash flow, leaving $8,900 for the old stockholders:

$$P_0 = \frac{\$110}{1.10} + \frac{\$89}{1.10^2} = \$100 + \$73.55 = \boxed{\$173.55}$$

Identical value. The mechanics: any increase in a dividend at one point in time is exactly offset by a decrease at another (each old share gets $10 more now but $11 = $10 × 1.1 less later, worth exactly zero in present value). Whatever payout pattern the firm chooses, the stock price stays the same.

5. Homemade Dividends

Shareholders can transform the firm's policy into any policy they prefer by trading on their own:

• Investor X prefers $100 at both dates but the firm pays $110 and $89: X reinvests the extra $10 at Date 1 (buying more Wharton stock); at 10 percent it grows to $11 by Date 2. Net cash flow: Date 1 = $110 − $10 = $100; Date 2 = $89 + $11 = $100.
• Investor Z prefers $110 and $89 but the firm pays $100 at both dates: Z sells $10 of stock at Date 1, giving up $10 × 1.1 = $11 at Date 2. Net cash flow: Date 1 = $100 + $10 = $110; Date 2 = $100 − $11 = $89.

Conclusion: dissatisfied stockholders can alter the firm's dividend policy to suit themselves, so there is no particular advantage to any one policy the firm might choose. Many corporations assist shareholders via automatic dividend reinvestment plans (DRIPs), e.g., McDonald's, Walmart, and Procter & Gamble.

6. A Test: Dividends vs. Dividend Policy

1. "Dividends are irrelevant"—false. If the dividend per share at one date is raised while every other date is held constant, the present value of future dividends rises and the stock price rises (achievable through productivity gains, tax savings, stronger marketing, etc.).
2. "Dividend policy is irrelevant"—true (in the simple case). Policy cannot raise the dividend at one date without changing the others; it only establishes the trade-off between dividends at different dates, and once time value is accounted for, the present value of the dividend stream is unchanged.

7. Real-World Factors Favoring a Low Payout

• Taxes: dividends are taxed as ordinary income; capital gains face lower rates and are taxed only upon sale (deferral), so their effective tax is lower. From 2003, dividend and long-term capital gains rates fell from a 35–39 percent maximum to 15 percent; in 2020 dividend tax rates were 0/15/20 percent by bracket—but deferral still leaves dividends with a higher effective tax. Ex-dividend evidence: the price should fall by about the dividend, slightly less after taxes—TransDigm's special $32.50 dividend (share price ~$600, about 5 percent) fell from a $597.78 close to a $568.00 open on the ex date (Dec 27, 2019), a $29.78 drop versus the ~$26 predicted at a 20 percent tax rate.
• Flotation costs: issuing new stock is expensive; the higher-payout firm must periodically sell stock to keep pace with the plowback of its twin, making high payout costly.
• Dividend restrictions: bond indentures often contain covenants capping dividends, and state law may bar dividends in excess of retained earnings.

Conclusion: with taxes and new-issue costs, pay dividends only after all positive-NPV projects are fully financed—the residual left over.

8. Real-World Factors Favoring a High Payout

• Desire for current income: retirees and others on fixed incomes are willing to pay a premium for dividend yield (Graham, Dodd & Cottle: "The discounted value of near dividends is higher than the present worth of distant dividends," and between two firms with the same earning power, "the one paying the larger dividend will almost always sell at a higher price"). Irrelevant in perfect markets (homemade dividends), but relevant with brokerage fees and other transaction costs—though mutual funds can "repack" at very low cost.
• Corporate investors: corporations receiving common or preferred dividends enjoy a 50 percent dividend exclusion (reduced from 70+ percent by the 2017 Tax Cuts and Jobs Act); capital gains get no such exclusion, so high-dividend, low-capital-gains stocks suit corporations—one reason corporations hold so much preferred stock.
• Tax-exempt investors: pension funds, endowment funds, and trust funds pay zero tax, so the tax arguments simply do not apply to them.

9. Information Content and the Clientele Effect

• Information content: stock prices rise on unexpected dividend increases and fall on unexpected cuts—not because the market likes high payouts, but because dividend changes convey information about expected future dividends. Managers cut dividends only with great reluctance, so a cut signals trouble and revises future dividend expectations (and the PV of the stream) downward. Evidence: U.S. Steel cut its dividend 80 percent (from $.20 to $.04 per year) on Dec 19, 2019, and lost about 11 percent of its value (volume jumped from ~14 million to ~43 million shares); Shell's cut (quarterly $.47 to $.16, freeing $10 billion) was followed by a ~13 percent fall; Nissan's ¥57-to-¥40 cut cost it ~7 percent. The reaction reflects revised expectations of future dividends, not the payout ratio itself—which makes it hard to interpret the effect of dividend policy.
• Clientele effect: different investor groups (wealthy individuals vs. corporations and tax-free institutions) prefer different dividend levels; a firm's policy merely attracts a particular clientele. Supply and demand do the rest: if 40 percent of investors prefer high dividends but only 20 percent of firms pay them, high-payout firms are in short supply, their prices rise, and low-payout firms switch until 40 percent of firms pay high dividends. In equilibrium, further policy changes are pointless—a firm cannot boost its share price by raising its payout unless an unsatisfied clientele exists, and there is no evidence that one does.

10. Key Takeaways

1. Dividends matter; dividend policy does not — stock value is the PV of future dividends, but "more now vs. more later" leaves that PV unchanged in perfect markets (Wharton: P₀ = $173.55 under both policies).
2. Homemade dividends are the mechanism — investors can replicate any policy by reinvesting or selling shares, so no policy confers an advantage.
3. Irrelevance is the benchmark; reality bends it — taxes and flotation costs argue for low payout (residual policy); current-income preference, the corporate dividend exclusion (50%), and tax-exempt investors argue for high payout; information content and clienteles explain price reactions to dividends without overturning the irrelevance of policy itself.

1. Core Idea

The dividend policy debate is about whether "cash today" is worth more than "capital gains tomorrow." Section 17.2 shows that in a perfect market dividend policy is irrelevant—shareholders can replicate any dividend schedule themselves by buying and selling stock (homemade dividends). The real world, however, has two frictions:

• Tax Differential Theory: dividends are taxed as ordinary income at a high rate and immediately; capital gains are taxed at lower rates and deferred until sale. Taxes and flotation costs make a low (or zero) payout optimal—Section 17.3.
• Bird-in-the-Hand Theory: investors dislike uncertainty—"a bird in the hand is worth two in the bush." A dividend today is certain; a capital gain tomorrow is risky, so investors pay a premium for high dividends—Section 17.4.

The book lists three positions (§17.5): (1) homemade dividends → dividend policy is irrelevant; (2) taxes + new issue costs → low payout is best; (3) desire for current income → high payout is best. This note covers the last two and their evidence.

2. Background: The Gap the MM Irrelevance Argument Leaves

The Wharton Corporation example: an all-equity firm, to be dissolved in two years, cash flow of $10,000 per year, 100 shares, 10 percent required return. Under the current policy (dividend of $100 each date):

$$P_0 = \frac{D_1}{(1+R)^1} + \frac{D_2}{(1+R)^2} = \frac{\$100}{1.10} + \frac{\$100}{1.10^2} = \$173.55$$

Under an alternative policy paying $110 per share at Date 1: total dividends of $11,000 exceed the $10,000 cash flow, so $1,000 of new stock is issued. New stockholders demand a 10 percent return and take $1,000 × 1.10 = $1,100 at Date 2, leaving old stockholders $8,900 ($89 per share):

$$P_0 = \frac{\$110}{1.10} + \frac{\$89}{1.10^2} = \$173.55$$

Any increase in a dividend at one date is exactly offset by a decrease at another, so the net effect is zero once time value is accounted for. Investor X (who wants $100/$100) reinvests the extra $10 at Date 1, which grows to $11 at 10 percent ($110 − 10 = $100; $89 + 11 = $100). Investor Z (who wants $110/$89) sells $10 of stock, giving up $10 × 1.1 = $11 at Date 2 ($100 − 11 = $89).

But this result rests on two assumptions: no taxes and no transaction costs. Sections 17.3 and 17.4 open each door in turn.

3. Tax Differential Theory: Why Taxes Favor Low Payout

The key tax feature (§17.3 TAXES): dividends were taxed as ordinary income, at up to 38.6 percent (2002); capital gains were taxed at a lower rate and deferred—tax is paid only when the stock is sold, so the present value of the tax is much smaller (the effective rate is "dragged down" by deferral).

Even after 2003 aligned the nominal rates, the deferral of capital gains tax still makes the effective tax rate on dividends higher for many investors—deferral lowers the present value of the tax. The 2020 schedule (0/15/20 percent on dividends) confirms the point: the deferral feature of capital gains never changed.

Corollary (§17.9, summary point 2): in a world with taxes and new issue costs, the firm should pay dividends only after all positive NPV projects have been fully financed—a low payout comes first.

4. Tax Differential Theory: Flotation Costs and Dividend Restrictions

Flotation costs (§17.3): issuing new stock is very expensive (Chapter 15). Consider two otherwise identical firms that differ only in payout percentage: the low-payout firm retains more cash, so its equity grows faster. For the two firms to stay identical, the high-payout firm must periodically sell new stock to catch up—each round costs real money. Hence a firm has an incentive to keep payout low.

Dividend restrictions:

• Bond indentures commonly include a covenant prohibiting dividends above some level (Chapter 7);
• State law may prohibit a corporation from paying dividends that exceed its retained earnings—a hard legal cap on payout capacity.

The tax edge of repurchases (§17.6, a direct application): an investor in the 28 percent bracket owns 100 shares. A $1 dividend → tax of $100 × .28 = $28. Under a repurchase: selling at $100 when the original cost was $60 means a gain of only $40 → capital gains tax .28 × $40 = $11.20. A shareholder pays tax only if (1) he actually chooses to sell and (2) he has a capital gain—the repurchase advantage is potentially large.

5. Tax Differential Theory: Ex-Dividend Price Behavior (Formula)

The ex-dividend price drop measures the size of the tax differential (the model of Problem 17.14; $P_0$ = price before ex, $P_X$ = ex-dividend price, $D$ = dividend per share, $T_P$ = marginal personal tax on dividends, $T_G$ = effective tax on capital gains):

$$\frac{P_0 - P_X}{D} = \frac{1 - T_P}{1 - T_G}$$

Intuition: the lower the capital gains tax relative to the dividend tax (case b), the more shareholders prefer keeping the money in the stock and the less the price falls on the ex date; the higher the gains tax (case c), the more shareholders value the dividend itself, and the drop can even exceed the dividend. Case d applies the 50 percent corporate exclusion (Section 7 below).

Evidence (TransDigm, December 2019): a special dividend of $32.50 per share on a stock near $600 (about 5 percent of the price). The stock closed at $597.78 on December 26 and opened at $568.00 on December 27—a drop of $29.78; with a 20 percent dividend tax the expected drop was about $32.50 × .80 = $26. The actual drop exceeded the expectation, showing the real tax structure is more complex than the simple assumption.

6. Bird-in-the-Hand Theory: Why High Payout Is Better

The classic statement comes from Graham, Dodd, and Cottle (§17.4 opening), two claims:

1. "The discounted value of near dividends is higher than the present worth of distant dividends." — a bird in the hand: today's dividend is certain cash; a remote, contingent capital gain is merely a bird in the bush.
2. Between "two companies with the same general earning power and same general position in an industry, the one paying the larger dividend will almost always sell at a higher price."

Two frequently cited supporting factors:

• Desire for current income: retired people and others living on fixed income (the proverbial widows and orphans) are willing to pay a premium for a higher dividend yield;
• Resolution of uncertainty: a dividend removes uncertainty—a future capital gain may never arrive, but cash already received cannot be lost.

7. The Objection, and Who Really Supports High Payout

The homemade dividend objection: an investor wanting current cash flow can sell a few low-dividend shares; one wanting low cash flow reinvests the dividend. In a world without transaction costs, a high current dividend policy is worth nothing (§17.4). In the real world, however, selling shares involves brokerage fees and other direct expenses, the stockholder's own time, and a natural (if not fully rational) fear of consuming out of principal—costs that buying high-dividend securities avoids altogether.

That said, financial intermediaries such as mutual funds can and do perform this "repackaging" at very low cost: buying low-dividend stocks and, through a controlled policy of realizing gains, paying investors a higher rate. This weakens the current-income argument considerably. The truly powerful high-payout supporters are two groups that do not suffer the dividend tax:

• Corporate investors: a corporation receiving dividends from another corporation enjoys a 50 percent (or more) dividend exclusion (reduced from 70 percent or more by the 2017 Tax Cuts and Jobs Act), and the exclusion does not apply to capital gains—so corporations are taxed unfavorably on gains. High-dividend, low-capital-gain stocks therefore suit corporations—which is why corporations hold a substantial share of outstanding preferred stock; interest has no similar exclusion, so corporations also hold high-yield stocks instead of long-term bonds.
• Tax-exempt investors: pension funds, endowment funds, and trust funds face a zero tax bracket—the whole tax discussion is moot, and high payout is attractive.

Conclusion (§17.4): individual investors may, for whatever reason, desire current income and be willing to pay the dividend tax; meanwhile some very large investors—corporations and tax-free institutions—may have a strong preference for high payout. The two forces coexist, and the clientele effect reconciles them: a firm's payout policy simply attracts its own clientele (§17.5).

8. Key Takeaways

1. Tax differential theory: low payout wins — dividends are taxed immediately as ordinary income (up to 38.6% in 2002; 0/15/20% in 2020), while capital gains are taxed at lower rates and deferred, so the effective rate is lower; with flotation costs, pay dividends only after all positive NPV projects are financed. The ex-dividend drop model $(P_0-P_X)/D = (1-T_P)/(1-T_G)$ quantifies the differential: the higher the gains tax relative to the dividend tax, the closer the drop gets to (or exceeds) D.
2. Bird-in-the-hand theory: high payout wins — "the discounted value of near dividends is higher than the present worth of distant dividends" (Graham–Dodd–Cottle); certainty preference and the desire for current income make investors pay a premium for high dividends. Homemade dividends dissolve the argument in a perfect market, but transaction costs and the fear of spending principal make it partly valid.
3. Who lines up where — high payout is supported by income-hungry individuals, tax-exempt institutions (pension, endowment, trust funds), and corporations with the 50 percent dividend exclusion; low payout by high-bracket individuals. Tax differential and bird-in-the-hand are not a contest—they operate on different investor groups, which is exactly where the clientele effect begins.

1. Core Idea

Signaling theory asks why the market is so sensitive to changes in dividends. Managers hold private information about their firm's prospects that outside investors lack. Because managers are extremely reluctant to cut dividends, a change in the dividend becomes a credible channel through which management sends a signal to the market. Empirically, stock prices rise on unexpected dividend increases and fall on unexpected dividend decreases—this is the information content effect of dividends.

The key distinction is between dividends themselves and dividend policy (the time pattern of payout). The price reaction to a dividend change reflects the market revising its expectations of the total future dividend stream, not a market preference for a particular payout ratio—so the information content of dividends makes the effect of dividend policy hard to interpret.

2. Market Reactions: Four Real Cases

The common thread: unanticipated dividend changes move prices in the same direction, and cuts are far more damaging than comparable increases—a cut is almost always forced, and amounts to management publicly admitting that the current policy cannot be sustained.

3. Why Dividends Are Credible Signals

A signal is credible only when sending it is costly:

1. Managers are extremely reluctant to cut dividends—in the survey by Brav et al. (2005), 93.8% of financial executives said "avoiding dividend cuts" affects their dividend decisions (Table 17.1), far ahead of any other factor.
2. Dividends are smoothed—in 2019, 1,808 U.S. companies increased dividends while only 309 cut them; Procter & Gamble had raised its dividend for 64 consecutive years through 2019, Colgate-Palmolive for 57, and 56 S&P 500 firms had raised for at least 25 consecutive years.
3. Implication: management raises the dividend only when confident that future earnings can sustain it. So—an increase signals optimism; a cut signals distress. The level of the dividend matters less than the change itself.

4. The Two-Part Signal (§17.7)

Why would a firm commit to cash dividends rather than a repurchase commitment? Committing to ongoing cash dividends sends a two-part signal:

1. A promise of profitability: the firm expects to remain profitable and able to pay on an ongoing basis, distinguishing it from weaker rivals. A firm cannot profit by faking this signal—if it later fails to pay (or pays only by tapping external financing), the market will punish it. The signal self-selects genuinely capable firms.
2. A promise not to hoard cash: committing to pay out cash now and in the future signals that the firm will not hoard free cash flow, reducing agency costs and enhancing shareholder wealth.

Historical footnote: after the dot-com crash of 2000 and the Enron and WorldCom scandals, investors lost trust in reported earnings; many firms initiated dividends precisely to signal that they had the cash to pay now and in the future—evidence and theory reinforcing each other.

5. Why Cash Dividends Rather Than Repurchase Commitments

A fixed repurchase strategy has two drawbacks:

1. Verifiability: a firm can announce an open-market repurchase and simply not do it, and shareholders would need a monitoring mechanism to detect the deception; a cash dividend needs no monitoring—the firm is forced to cut and mail checks four times a year, year after year.
2. Forced overvalued buybacks: if managers (as insiders) believe their stock is overvalued, a fixed repurchase commitment forces them to buy back overpriced stock—a negative NPV investment.

6. Dividends versus Dividend Policy: Revisiting Irrelevance

The two-period Wharton Corporation example (§17.2) is the benchmark. An all-equity firm liquidates in two years with $10,000 of cash flow each period, 100 shares outstanding, and a 10 percent required return:

$$P_0 = \frac{D_1}{1+R} + \frac{D_2}{(1+R)^2} = \frac{\$100}{1.10} + \frac{\$100}{1.10^2} = \$173.55$$

If instead the firm pays $110 per share at Date 1 (raising the extra $1,000 by issuing stock; new stockholders demand a 10 percent return and take $1,100 of the Date-2 cash flow, leaving $8,900, or $89 per share, for old stockholders):

$$P_0 = \frac{\$110}{1.10} + \frac{\$89}{1.10^2} = \$173.55$$

The price is unchanged—in a simple world, dividend policy is irrelevant (shareholders create homemade dividends). This matches the textbook quiz: "dividends are irrelevant" is false, but "dividend policy is irrelevant" is true. In the real world, however, the information content effect makes this hard to test: prices rise with dividends simply because expectations of future dividends are revised upward, not because the market prefers a higher payout ratio.

7. The Clientele Effect (Same Section)

Different investor groups desire different dividend levels: high-tax individuals prefer low payout; corporations (with at least a 50 percent dividend exclusion) and tax-exempt institutions prefer high payout. A firm's dividend policy merely attracts a particular clientele. If 40 percent of investors prefer high dividends but only 20 percent of firms pay them, high-dividend firms are in short supply and their prices rise—until 40 percent of firms pay high dividends and the market clears. The clientele effect implies that, once every clientele is satisfied, any individual firm's payout ratio is not very important.

8. Curriculum Ideology and Politics

• Integrity is a precondition for signaling. The textbook's conclusion—"a firm cannot benefit by trying to fool the market, because it will ultimately be punished when it cannot pay"—echoes the Chinese virtue that "a person without integrity cannot stand; a business without integrity cannot thrive." Signaling theory says: in the long run, only firms that are genuinely capable and true to their word keep the market's trust; firms that try to raise money with false signals (e.g., exaggerated payout promises) will ultimately be voted down by the market.
• Chinese practice: steadily tightening payout regulation. The CSRC's Guidelines No. 3 for Listed Companies—Cash Dividends (issued 2013, revised 2022) requires listed companies to specify cash dividend policies in their charters and to enhance the transparency and stability of payouts. In April 2024, the State Council issued the new "Nine National Guidelines" (Opinions on Strengthening Regulation, Preventing Risks, and Promoting High-Quality Development of the Capital Market), explicitly calling to "strengthen supervision of cash dividends" and to encourage "multiple dividends per year, advance dividends, and pre-Spring Festival dividends."
• Investor protection. A dividend commitment is a contractual promise to minority shareholders. Kweichow Moutai, for example, has paid a cash dividend every year since its 2001 listing—its 2022 annual payout of RMB 27.511 per share totaled about RMB 34.56 billion—earning long-term shareholder trust through stable, deliverable returns and serving as a benchmark of value investing in the A-share market. This is "keeping one's word" institutionalized in both regulation and corporate behavior.

9. Key Takeaways

1. Dividends are signals, not ends — unexpected increases raise prices and cuts lower them; but the market is revising expectations of future dividends, not expressing a preference for payout ratios.
2. Credibility comes at a cost — 93.8 percent of executives avoid dividend cuts, and heavy dividend smoothing (1,808 increases vs. 309 cuts in 2019) make dividends a signal that is hard to fake.
3. Cash dividends hold a unique position — the two-part signal (profitability plus no cash hoarding) and built-in verifiability explain why repurchases cannot fully replace cash dividends.
4. Integrity creates value — being true to shareholders is the foundation of long-term firm value and of a healthy capital market.

1. Core Idea: The Textbook Conclusions and the Chinese Context

Section 17.7 distills five stylized facts: ① aggregate dividends and repurchases are massive and growing; ② dividends are heavily concentrated in a small number of large, mature firms; ③ managers are very reluctant to cut dividends; ④ managers smooth dividends, raising them slowly as earnings grow; and ⑤ stock prices react to unanticipated dividend changes. All five hold for Chinese listed companies—but with one extra dimension that the U.S. does not have: deep regulatory involvement. Dividend behavior in China is the joint product of market forces and institutional guidance, and understanding that is the key to this topic.

Moral education point: cash dividends are the most direct way listed companies reward investors; sustained, stable payout is the essence of a "investor-centered" capital market and a micro-level expression of shared prosperity.

2. Institutional Background: Four Milestones of Regulation

Moral education point: from "dividends to refinance" to "no dividends, no reductions," the regulatory logic is consistent—putting shareholder returns at the center of capital market design.

3. Characteristic 1: Dividends Rising in Both Total Amount and Participation

Aggregate cash dividends of A-share listed companies (annual basis, including interim dividends):

In FY2023, about 3,600+ companies paid dividends—roughly 70 percent of the ~5,300 listed firms. This contrasts sharply with the U.S., where the proportion of dividend payers declined (65% in 1978 → 19% in 2000) while in China it rose under regulatory push.

4. Characteristic 2: Heavy Concentration in Large Mature Firms (Same as the Textbook)

The textbook notes that in 2000 about 80 percent of U.S. dividends were paid by just 100 firms. China shows the same "80/20" pattern: banks, oil & petrochemicals, coal, and liquor giants contribute most payouts. Two worked examples (payout ratio = cash dividends ÷ net income):

• ICBC (FY2023): ¥3.064 per 10 shares → ¥0.3064/share; ~356.4 billion shares → total dividends $= 0.3064 \times 356.406\ 亿 = \textbf{≈ ¥109.2\ billion}$; net income ≈ ¥365.1 billion → payout ratio ≈ 30%.
• Kweichow Moutai (FY2023): ¥308.76 per 10 shares → ¥30.876/share; 1.256 billion shares → $= 30.876 \times 1.256\ 亿 = \textbf{≈ ¥38.8\ billion}$.
• China Shenhua (FY2022): ¥2.55/share → $2.55 \times 19.869\ 亿 = ¥50.67\ 亿元$; net income ¥69.626 billion → payout = 50.67/69.63 ≈ 72.8%.

This is exactly the textbook's life-cycle theory: mature firms with stable earnings and ample free cash flow pay high dividends, while young growth firms (e.g., STAR Market listings) pay little or none and reinvest.

5. Characteristic 3: High-Yield "Dividend Assets" in Demand

Dividend yield = dividend per share ÷ share price. Shenhua at ¥2.55/share and a share price near ¥28 in early 2023 yielded about 9 percent; bank stocks commonly yield above 5 percent. In 2024 the CSI 300 dividend yield briefly exceeded 3 percent, above the 10-year government bond yield (below ~2.3%)—making "bond-proxy" dividend assets (banks, coal, utilities, toll roads) a major allocation for institutions and individuals.

6. Characteristic 4: Strong Market Reactions to Dividend Signals—The Gree Case

The textbook reports U.S. Steel's 80 percent dividend cut (from $0.20 to $0.04) on December 19, 2019, knocked about 11 percent off its stock price—unanticipated dividend changes are powerful signals. China's landmark episode is Gree Electric's 2018 no-dividend controversy:

• April 2018: Gree announced no dividend for FY2017 (its first omission in 11 years) → the Shenzhen Stock Exchange issued an inquiry letter the same day, and the market reacted sharply;
• Gree replied that it was planning major investments (new energy, chips) and committed to paying at least 50 percent of annual net income in cash dividends for 2018–2020; it actually paid ¥15 per 10 shares for FY2018.

Moral education point: paying dividends is not merely a financial decision—it is about respect for and honesty toward minority investors; erratic payout expectations destroy corporate credibility.

7. Characteristic 5: "Tightwads" and "Liquidation-Style Dividends" Coexist

• "Tightwad" firms (tie gong ji): some firms never paid dividends for years. In 2017 regulators publicly criticized chronic non-payers (e.g., Jinbei Auto), and public pressure forced reforms;
• "Liquidation-style dividends": in 2023–2024 a few firms declared payouts far exceeding net income, suspected of funneling cash to controlling shareholders (who receive dividends pro rata), prompting regulators to scrutinize abnormal payouts.

The backdrop is concentrated ownership: Chinese listed firms are typically controlled by a large shareholder ("one-share dominance"), so high payouts cut both ways—either rewarding shareholders or serving as a channel for the controlling shareholder to extract cash. Moral education point: dividend rules must balance controlling and minority shareholders and prevent well-intended policies from being abused—a micro test of fairness and investor protection.

8. Characteristic 6: New Tools—Buybacks and Interim Dividends

The textbook shows buybacks growing faster than dividends; China's buybacks started late and remain much smaller than dividends, but policy is accelerating them:

• September 2024: the PBoC created a buyback-and-holdings refinancing facility—an initial quota of ¥300 billion at an annual rate of 1.75% to support buybacks and controlling-shareholder increases;
• Interim dividends: after the 2023 guideline simplified interim dividend procedures, over 900 companies paid interim dividends in 2024, up sharply—payout frequency is shifting from once a year to twice a year.

9. China–U.S. Comparison and Key Takeaways

Key takeaways:

1. Aggregate facts are institutional: China's total dividends and participation both rose (≈¥2.4 trillion and ≈70% of firms in 2024), rooted in the "dividends-refinancing/reduction" linkage built since 2001—institutional dividend is the Chinese characteristic;
2. Structure follows the theory: concentration in large mature firms (ICBC ¥109.2 billion, Moutai ¥38.8 billion, Shenhua's 72.8% payout) matches the textbook's life-cycle theory exactly;
3. Governance is about balance: with concentrated ownership, high payouts can reward or extract—Gree and liquidation-style dividends show that dividend policy is ultimately corporate governance, and investor protection keeps driving the refinement of payout rules.

1. Core Idea

Financial leverage refers to the extent to which a firm relies on debt: the more debt financing in its capital structure, the more financial leverage it employs. Leverage does not change the firm's assets or operations, but it magnifies shareholder payoffs (EPS and ROE) in response to changes in operating performance (EBIT)—shareholders gain more in good times and lose more in bad times. EPS–EBIT analysis quantifies this magnification: plot EPS against EBIT for each capital structure, then find where the two lines cross—the break-even (indifference) EBIT—to judge when leverage helps and when it hurts. Taxes are ignored throughout this section.

2. The Trans Am Corporation Example

Trans Am is currently all-equity: assets $8 million, share price $20, 400,000 shares outstanding. The CFO considers restructuring: issue $4 million of debt at 10 percent and use the proceeds to repurchase $4{,}000{,}000/$20 = 200,000 shares, leaving 200,000:

The restructuring merely swaps equity for debt—assets are unchanged—but adds a fixed annual interest bill of $4{,}000{,}000 × 10% = $400,000.

3. EPS and ROE under Three Scenarios (Table 16.4)

EBIT of $500,000 (recession), $1,000,000 (expected), and $1,500,000 (expansion):

Check the expansion case: with no debt, EPS = $1{,}500{,}000/400{,}000 = $3.75 and ROE = $1{,}500{,}000/$8{,}000{,}000 = 18.75%. With debt, interest of $400,000 leaves net income of $1.1 million; EPS = $1{,}100{,}000/200{,}000 = $5.50 and ROE = $1{,}100{,}000/$4{,}000{,}000 = 27.5%, well above the 18.75 percent no-debt figure.

The levered EPS range ($0.50–$5.50) is far wider than the unlevered range ($1.25–$3.75): leverage magnifies both gains and losses.

4. The EPS–EBIT Diagram: Slope and Sensitivity

Plotting EPS against EBIT (Figure 16.1) gives two straight lines:

• No-debt line: EPS = EBIT/400,000, through the origin (EPS = 0 when EBIT = 0); every $400,000 of extra EBIT raises EPS by $1
• With-debt line: EPS = (EBIT − $400,000)/200,000; at EBIT = 0, EPS = −$2 (interest must be paid regardless of profits); at EBIT = $400,000, EPS = $0; every $400,000 of extra EBIT raises EPS by $2

The levered line is twice as steep: EPS is twice as sensitive to EBIT under leverage—the sensitivity ratio equals assets/equity = $8M/$4M = 2. This is the essence of financial leverage.

5. Break-Even (Indifference) EBIT

Set the two EPS expressions equal:

$$\frac{\text{EBIT}^}{400{,}000} = \frac{\text{EBIT}^ - 400{,}000}{200{,}000} \Rightarrow \text{EBIT}^ = 2 \times (\text{EBIT}^ - 400{,}000) = \$800{,}000$$

General form: $\text{EBIT}^* = \dfrac{N_0 \times I}{N_0 - N_1}$, where $N_0$ and $N_1$ are shares before and after the buyback and $I$ is annual interest.

At EBIT = $800,000, EPS is $2 under either structure. Intuition: with no debt, ROE = $800{,}000/$8{,}000{,}000 = 10 percent—exactly the interest rate on the debt, so the firm earns just enough to pay the interest. Above $800,000, leverage is beneficial; below it, it is not.

Example 16.1 (MPD): $1 million of debt at 9 percent costs $90,000 of interest; the proceeds buy back 50,000 shares at $20, leaving 150,000. EBIT/200,000 = (EBIT − 90,000)/150,000 gives EBIT = (4/3) × (EBIT − 90,000) = $360,000, where EPS is $1.80 in both structures. Management must expect EBIT above $360,000 for the restructuring to raise EPS.

6. Four Conclusions on Leverage

Ms. Morris draws four observations:

1. The effect of leverage depends on EBIT: when EBIT is high, leverage is beneficial.
2. Under the expected scenario, leverage increases both ROE and EPS.
3. Shareholders bear more risk under the proposed structure—EPS and ROE are far more sensitive to EBIT.
4. Because leverage affects both the expected return and the riskiness of the stock, capital structure is an important consideration.

The first three are clearly correct; the fourth does not necessarily follow—see homemade leverage below.

7. Homemade Leverage

Shareholders can replicate corporate leverage by borrowing on their own (Table 16.5). If Trans Am adopts the proposed structure, an investor buys 100 shares for $2,000 and earns $50/$300/$550. If it does not, the investor personally borrows $2,000 at 10 percent (personal D/E = $2{,}000/$2{,}000 = 1, matching the proposed structure), buys 200 shares with $4,000 (EPS $1.25/$2.50/$3.75 → earnings $250/$500/$750), pays $200 of interest, and nets $50/$300/$550—identical payoffs.

To "unlever" (Example 16.2): if the firm adopts the proposed structure but the investor prefers the original, sell 50 shares for $1,000 and lend the proceeds at 10 percent: 50-share earnings of $25/$150/$275 plus $100 of interest = $125/$250/$375, exactly the original structure's payoffs on 100 shares at EPS of $1.25/$2.50/$3.75.

Because investors can always create or undo leverage personally, the firm's choice of capital structure is irrelevant in this simple, tax-free world—a preview of M&M Proposition I.

8. Business Risk versus Financial Risk (M&M Proposition II Preview)

M&M Proposition II (no taxes): $R_E = R_A + (R_A - R_D) \times (D/E)$—the cost of equity depends on the required return on assets $R_A$, the cost of debt $R_D$, and the debt-equity ratio. Equity's total risk has two parts: business risk, set by the firm's assets and operations and unaffected by capital structure; and financial risk, $(R_A - R_D) \times (D/E)$, entirely determined by financial policy. Example 16.3 (Ricardo): WACC = 12 percent, cost of debt 8 percent. At 80 percent equity (D/E = .25), $R_E = .12 + (.12 - .08) \times .25 = 13\%$ and WACC stays 12 percent; at 50 percent equity (D/E = 1), $R_E = 16\%$ and WACC is still 12 percent. The cheapness of debt is exactly offset by the higher cost of equity—WACC is independent of capital structure.

9. Key Takeaways

1. Leverage is an amplifier — it leaves assets and EBIT unchanged but doubles the sensitivity of EPS/ROE to EBIT (slope ratio = $8M/$4M = 2), magnifying gains and losses alike.
2. The indifference point is the dividing line — leverage helps when EBIT exceeds it (Trans Am: $800,000) and hurts below it; to judge whether a restructuring raises EPS, compare expected EBIT with the break-even level.
3. Leverage can be homemade — investors can replicate any corporate capital structure with personal borrowing at the same D/E, so in a perfect market the firm's capital structure is irrelevant—setting up the M&M framework.

1. Core Idea

Financial leverage is the extent to which a firm relies on debt. Leverage does not change EBIT, but it amplifies swings in shareholder payoffs (EPS and ROE): interest is a fixed charge, so every dollar of EBIT above it goes to shareholders. A double-edged sword—leverage helps when EBIT is high and hurts when EBIT is low.

Whether leverage changes firm value and the cost of capital depends on the assumptions—three layers, and three modeling levels:

1. No taxes (§16.3, M&M I & II): leverage does not affect firm value or the WACC—investors replicate any capital structure with homemade leverage.
2. Corporate taxes (§16.4): deductible interest creates an interest tax shield, $V_L = V_U + T_C \times D$; leverage raises value and lowers the WACC; taken alone, the optimum is 100 percent debt.
3. Taxes plus bankruptcy costs (§16.5-16.6, static theory): the shield trades off against distress costs, giving an interior optimum D*.

Modeling in Excel/Python means computing and charting the EPS–EBIT lines, the break-even EBIT, the present value of the tax shield, and $V_U$, $V_L$, and the WACC.

2. Leverage, EPS, and ROE: The Trans Am Corporation

Assets $8,000,000, no debt, 400,000 shares at $20; the proposal issues $4M of debt at 10 percent (interest $400,000) to repurchase $4M/$20 = 200,000 shares, leaving 200,000 shares and D/E = 1. Three scenarios (no taxes; NI = EBIT or EBIT − $400,000; EPS = NI/shares, ROE = NI/equity $8M or $4M, Table 16.4):

Check (expansion): $1.5M/400,000 = $3.75; levered NI = $1.1M, $1.1M/200,000 = $5.50 and $1.1M/$4M = 27.5%. Leverage widens EPS from $1.25–$3.75 to $0.50–$5.50 and ROE from 6.25%–18.75% to 2.50%–27.50%—the swings are magnified; that is what leverage does.

3. EPS–EBIT Lines and the Break-Even EBIT

With no taxes, EPS is linear in EBIT: $EPS = (EBIT - I)/N$.

• No-debt line $EPS = EBIT/400{,}000$: through the origin, slope 1/400,000—every $400,000 rise in EBIT adds $1 to EPS;
• Levered line $EPS = (EBIT-400{,}000)/200{,}000$: EPS = −$2 at EBIT = 0 (interest must be paid anyway), slope twice as steep—every $400,000 adds $2.

The lines cross at the break-even (indifference) EBIT:

$$EBIT/400{,}000 = (EBIT-400{,}000)/200{,}000 \;\Rightarrow\; EBIT^* = \$800{,}000,\quad EPS = \$2$$

Intuition: at EBIT = $800,000 the all-equity ROE is $800K/$8M = 10 percent—exactly the interest rate; the firm earns just enough to pay interest. Above this point leverage helps; below, it hurts. General formula (old: N1 shares, interest I1; new: N2, I2):

$$EBIT^* = \frac{N_1 I_2 - N_2 I_1}{N_1 - N_2}$$

MPD: $1M of debt at 9 percent (interest $90,000) repurchases 50,000 shares; BDJ: debt rises $80M → $125M (interest $7.2M → $11.25M), repurchasing 1M shares.

4. Homemade Leverage: Why Capital Structure Is "Irrelevant"

An investor wants to hold $2,000 of stock. If the firm adopts the proposal, 100 shares pay $50/$300/$550; if not, the investor borrows $2,000 at 10 percent and, with his or her own $2,000, buys 200 shares, then pays $200 interest (Table 16.5):

Both strategies have the same net cost ($2,000): the firm's D/E is 1, and the investor replicates it with $2,000 of own equity plus $2,000 of personal borrowing. The reverse—unlevering (Example 16.2): holding 100 shares of the levered firm, sell 50 shares for $1,000 and lend it at 10 percent—$25/$150/$275 plus $100 interest = $125/$250/$375, exactly the all-equity payoffs. Conclusion: the size of the pie does not depend on how it is sliced (M&M Proposition I).

5. M&M without Taxes: Cost of Capital and Leverage

Proposition I (no taxes): $V_L = V_U$; the WACC is independent of capital structure. Proposition II (no taxes):

$$R_E = R_A + (R_A - R_D) \times (D/E)$$

The cost of equity rises linearly with D/E, slope $(R_A − R_D)$; $R_A$ reflects business risk (inherent in assets and operations), while $(R_A − R_D)(D/E)$ is financial risk (determined entirely by financial policy)—equity risk = the sum of the two.

Ricardo Corporation (Example 16.3, $R_A = 12\%$, $R_D = 8\%$):

• 80% equity: D/E = .25 → $R_E = .12 + .04 \times .25 = 13\%$; WACC = $.80 \times .13 + .20 \times .08 = 12\%$
• 50% equity: D/E = 1 → $R_E = .12 + .04 \times 1 = 16\%$; WACC = $.50 \times .16 + .50 \times .08 = 12\%$

The WACC is 12 percent either way: the "cheapness" of low-cost debt is exactly offset by the rising cost of equity.

6. M&M with Corporate Taxes: The Interest Tax Shield

Firms U (unlevered) and L (levered, $1,000 of perpetual debt at 8 percent) have identical assets; EBIT is $1,000 forever, $T_C = 21\%$:

L's cash flow exceeds U's by $16.80 = $80 × 21% = the interest tax shield; it has the same risk as the debt, so it is discounted at $R_D = 8\%$ (perpetuity):

$$PV(\text{tax shield}) = \frac{T_C \times D \times R_D}{R_D} = T_C \times D = .21 \times \$1{,}000 = \$210$$

Proposition I with taxes: $V_L = V_U + T_C \times D$. With $R_U = 10\%$: $V_U = \$790/.10 = \$7{,}900$, $V_L = \$7{,}900 + .21 \times \$1{,}000 = \$8{,}110$, equity E = $7,110—firm value rises $.21 per $1 of debt.

Proposition II with taxes: $R_E = R_U + (R_U - R_D)(D/E)(1 - T_C)$

$$R_E = .10 + (.10-.08) \times \frac{\$1{,}000}{\$7{,}110} \times (1-.21) = 10.22\%$$

$$WACC = \frac{7{,}110}{8{,}110} \times .1022 + \frac{1{,}000}{8{,}110} \times .08 \times .79 = 9.74\% < 10\%$$

More debt, lower WACC, so with taxes alone the optimum is 100 percent debt (corrected in §16.5-16.6 by bankruptcy costs and the static theory). Format Co. (Example 16.4: EBIT $126.58, $T_C=.21$, D=$500$, $R_U=20\%$, $R_D=10\%$): $V_U = \$100/.20 = \$500$, $V_L = \$605$, E = $105, $R_E = .20 + .10 \times (\$500/\$105) \times .79 = 57.62\%$, $WACC = (\$105/\$605)(.5762) + (\$500/\$605)(.10)(.79) = 16.53\% < 20\%$.

Real-world caveat: the 2017 Tax Cuts and Jobs Act caps the net interest deduction at 30 percent of EBITDA (2018–2021) and 30 percent of EBIT thereafter (CARES Act: 50 percent temporarily for 2019–2020); disallowed interest carries forward—the shield is not unlimited.

7. Modeling in Excel / Python

Excel skeleton (Trans Am): inputs—assets $8M, shares 400,000, rate 10%, debt $4M (or derive D from a target D/E); new shares =400000-debt/20; interest =debt*rate; EPS =(EBIT-interest)/shares (multiply by 1−tax with taxes); break-even =(N1*I2-N2*I1)/(N1-N2), or set the EPS difference to zero with Goal Seek, or use a Data Table with EBIT as the row input to chart both EPS–EBIT lines.

Excel Master IT! (TL Corporation): assets $40M, price $25, 1.6M shares; EBIT $1.8M (recession) / $3M (expected) / $4.3M (expansion); debt mixes short-term (3%) and long-term (8%) with ST/LT = .20 (short-term = 1/6) → $R_D = \frac16 \times 3\% + \frac56 \times 8\% = 7.17\%$. Use a spinner to vary D/E from 0 to 10 in steps of .1, graph EPS versus EBIT, find the break-even, and show the debt mix with a pie-in-pie chart. Check at D/E = 1: D = $20M, interest ≈ $1.43M, 800,000 shares repurchased leaving 800,000, EBIT* = 2 × interest ≈ $2.87M < the expected $3M, so leverage pays in the expected state.

Python (outputs match the book's numbers):

def eps(ebit, debt, rd, shares):
    return (ebit - debt * rd) / shares           # EPS = (EBIT - I) / N

def be_ebit(n1, i1, n2, i2):
    return (n1 * i2 - n2 * i1) / (n1 - n2)       # break-even EBIT: EPS1 = EPS2

be_ebit(400_000, 0, 200_000, 400_000)                 # 800,000   Trans Am
be_ebit(200_000, 0, 150_000, 90_000)                  # 360,000   MPD
be_ebit(10_000_000, 7_200_000, 9_000_000, 11_250_000)  # 47,700,000 BDJ

TC, EBIT, RU, RD, D = .21, 1000.0, .10, .08, 1000.0
VU   = EBIT * (1 - TC) / RU              # 7,900
VL   = VU + TC * D                       # 8,110   (M&M I with taxes)
E    = VL - D                            # 7,110
RE   = RU + (RU - RD) * (D / E) * (1 - TC)  # 0.1022 (M&M II with taxes)
WACC = E / VL * RE + D / VL * RD * (1 - TC) # 0.0974

Pitfalls: ① the denominator $N_1 − N_2$ is the number of shares repurchased; the EPS slope is 1/N, so buybacks steepen the line—the source of amplification; ② $T_C \times D$ requires the perpetual-debt assumption—discount maturing debt year by year; ③ with taxes, multiply EPS's numerator by $(1-T_C)$; the shield lowers the break-even EBIT.

8. Key Takeaways

1. Leverage magnifies gains and losses — above the break-even EBIT, leverage pays (Trans Am $800,000, MPD $360,000, BDJ $47.7M); below it, it does not.
2. Irrelevance follows from homemade leverage — with no taxes $V_L = V_U$ and the WACC is constant; in $R_E = R_A + (R_A-R_D)(D/E)$ the rising equity cost exactly offsets cheap debt (both Ricardo structures have a 12% WACC).
3. The tax shield is where leverage creates value — deductible interest is worth $T_C \times D$ (Firm L's extra $16.80 per year is worth $210; WACC falls to 9.74%); but taxes alone imply 100 percent debt, so the real-world optimum comes from bankruptcy costs—always state the assumptions when modeling.