A.6 Capital Structure & Corporate Finance

Basic Prerequisites: Financial Statements & Accounting (the three statements) and Core Financial Ratios (the leverage, coverage, and ROIC ratios this folder explains). (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

Every firm must decide how to pay for itself: debt or equity, in what mix, with what payout policy. This folder is about the corporate-finance theory underneath the leverage and coverage ratios in every statement. The single organizing idea - and the null hypothesis every corporate-finance question starts from - is Modigliani & Miller’s (1958) irrelevance theorem: in a frictionless world (no taxes, no bankruptcy costs, no information asymmetries), how you finance the business changes nothing about what it is worth. Financing just slices a fixed value pie into differently-shaped claims.

The whole of corporate finance is then the study of when that frictionless world breaks - and it breaks in exactly four places, each of which is a genuine source of value (or destruction):

1. Taxes → interest is tax-deductible, so debt carries a tax shield worth $\tau D$.
2. Financial-distress costs → leverage magnifies the risk of bankruptcy, and distress is expensive.
3. Information asymmetry → managers know more than investors, which makes issuing equity a “bad news” signal and forces a pecking order (internal → debt → equity).
4. Agency costs → managers’ interests diverge from shareholders’, so the payout of free cash flow matters (Jensen 1986), and debt can serve as a disciplining device.

This folder is the hub. It (a) gives the fast key-results lookup table below - the MM propositions, WACC, the tax shield, the seniority ladder, dilution, and the buyback/EPS arithmetic (job #1 of this folder), and (b) routes to six sub-pages that walk from raw intuition (debt vs. equity, equity as the residual claim) through the MM theorem itself, the seniority/priority structure, dilution & buybacks, failure modes (death spirals, agency costs), and the advanced layer (pecking order, agency theory, the trade-off theory).

The one-sentence essence. “Financing is irrelevant only in a world without taxes, distress, information, and agency - in ours, capital structure is the art of trading the tax shield of debt against the distress and agency costs it invites, and of returning free cash flow when it cannot be reinvested at the cost of capital.”

Audience arc: beginner reads what debt vs. equity mean and who gets paid first; intermediate reads the MM theorem, WACC, and why leverage changes (and doesn’t change) value; expert reads agency costs, the pecking order, and the trade-off of optimal capital structure. The sub-pages below are ordered for exactly that climb.

2. Mathematical Ground Truth & Lookup Table

Notation: $X$ expected operating income (EBIT), $r$ rate of interest on debt, ${\rho }_k$ the capitalization rate (“cost of capital”) for a pure-equity stream of class $k$, $D$ market value of debt, $S$ market value of equity, $V=S+D$ market value of the firm, $\tau$ corporate tax rate, WACC weighted average cost of capital.

The MM axioms (1958). No taxes, no transaction or bankruptcy costs, equal borrowing rates for firms and individuals, and homogeneous risk classes (firms in the same class have proportional expected earnings). Under these, the market value of a firm is the expected return capitalized at its class rate - regardless of capital structure.

(All lookup values computed and reproduced exactly in §3; the sample firm used there is the Modigliani–Miller 1958 fn-12 firm, X = 1,000, r = 5%, ρ = 10%, D = 4,000.)

Critical scaling caveat. $r_E$, $r$, ${\rho }_k$, $\tau$, and WACC are decimals/percent; $D/S$ and $\tau D/V$ are pure ratios; $\tau D$ is a currency value. Mixing percentage and decimal inputs into the tax shield or the WACC formula is the single most common error in this table (the hub engine in §3 keeps everything decimal).

3. Computational Implementation - the formula engine

Runs on the standard library only. It reproduces every headline lookup value from the table above and - the part that proves the math - it checks the two MM consistency identities: Proposition II’s $r_E$ equals the definition $(X-rD)/S$, and Proposition I’s WACC is flat regardless of leverage.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the folder’s failure-mode analysis lives in 05 · Failure Modes & Practice. In one line each:

1. The “leverage is always good” mistake. The tax shield is real but the distress cost is realer - leverage amplifies downside too (the §1 good 52% / bad 4% vs. all-equity 30% / 6%). The MM axiom says leverage creates nothing; it only re-slices risk.
2. Issuing equity is a bad-news signal. Because managers sell shares only when they think they’re not too cheap, an equity issue is interpreted as “the shares are overpriced” (Myers–Majluf) - which is why firms prefer debt to external equity.
3. Buybacks and EPS accretion are not value creation. Retiring shares mechanically raises EPS, but if the cash spent was earning at the cost of capital, no value was created - only the EPS number grew.
4. Seniority is everything in distress. Equity is the residual claim - paid last, after every creditor is whole. At moderate liquidation values equity gets nothing, which is exactly what “equity is the riskiest claim” means.

5. References

• Modigliani, Franco & Miller, Merton H.: “The Cost of Capital, Corporation Finance and the Theory of Investment” (AER, 1958, 48(3), 261–297)
• Myers, Stewart C. & Majluf, Nicholas S.: “Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have” (JFE, 1984, 13(2), 187–221)
• Jensen, Michael C. & Meckling, William H.: “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure” (JFE, 1976, 3(4), 305–360)
• Jensen, Michael C.: “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers” (AER, 1986, 76(2), 323–329)
• Brealey, Myers & Allen, Principles of Corporate Finance
• Graham, Benjamin & Dodd, David, Security Analysis (6th ed., 2008)

6. Connected Graph Bridges

• Foundational base: Financial Statements & Accounting · Core Financial Ratios - Liquidity & Leverage
• Sibling topic: Equity Valuation - DCF & WACC (WACC is the discount rate this folder explains) · Fundamental Analysis & Screening
• Sub-pages (in-folder): 01 From Zero · 02 Modigliani–Miller · 03 Debt, Equity & Seniority · 04 Dilution & Buybacks · 05 Failure Modes & Practice · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05