A.6.3 Debt, Equity & Seniority

Basic Prerequisites: 01 · From Zero and 02 · Modigliani–Miller.

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1. Intuition & Practical Objective

Financing instruments are ranked claims on the same future cash flows, and their rank determines almost everything about them: how much they are paid, how risky they are, and what return they must offer. The ranking is the priority (seniority) structure. Getting it right matters because the difference between “a claim that is protected” and “a claim that eats the leftovers” is the difference between a bond and a stock.

The ladder, from most to least protected (this is the user’s own seniority ordering, standard across every capital market):

$$\underset{\text{paid first}}{\underbrace{\text{senior debt}}}\prec \underbrace{\text{junior debt}}\prec \underbrace{\text{mezzanine}}\prec \underbrace{\text{convertible}}\prec \underset{\text{residual, paid last}}{\underbrace{\text{common equity}}}$$

(where $\prec$ reads “is paid before” - i.e. leftmost is most senior).

Every rung is paid only after all rungs above it are fully satisfied, in operating cash flow and in liquidation. Common equity sits at the bottom of the ladder - it is the residual claim, the “paid last” rung of 01. Everything senior to it is, in effect, a claim against equity’s share.

The practical objective is to see leverage through this ladder:

• Leverage is the share of the capital base funded by claims senior to equity - debt that must be serviced before shareholders see a dollar. Financial risk is the risk those senior claims impose on equity: higher leverage means more fixed obligations ahead of the residual, so equity’s claim becomes both thinner and more volatile (Prop II of 02).
• Different seniority rungs bear different risk at different distress levels. Senior debt is almost always repaid; junior/mezzanine is repaid only if assets cover it; convertible pays as debt or converts to (diluting) equity; equity is wiped out first in bankruptcy. So each rung’s required return is a function of its place in the ladder.
• The accounting statement of all this is the leverage/coverage ratio set (EBITDA, Interest Coverage) - they measure how much claim sits above equity and how comfortably it is serviced.

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2. Mathematical Ground Truth & Derivations

Priority as a waterfall. Given liquidation value $A$ and claims $C_1>C_2>\cdots >C_n$ ordered by seniority (largest claim = most senior), each claim $C_i$ recovers

$${\text{recovery}}_i=\min (C_i,\max (0,A-\sum _{k<i}{C}_k)).$$

Equity, the last rung, receives the strict residual:

$$\text{equity recovery}=\max (0,A-\sum _{k=1}^{n-1}{C}_k).$$

Two immediate consequences, both first-principles: (1) equity is worth zero for any liquidation value below the sum of all senior claims; (2) senior claims are shielded from losses - a decline in $A$ first erodes equity, then convertible, then mezzanine, then junior debt, and only last senior debt. This is precisely why senior debt can carry the lowest rate: its downside is minimal.

Leverage and financial risk (Prop II restated). With $S$ equity, $D$ debt, ${\rho }_k$ the class equity cost, $r$ the debt rate:

$$r_E={\rho }_k+({\rho }_k-r)\frac{D}{S}.$$

The financial-risk premium $({\rho }_k-r)D/S$ is the reward for standing below $D$ of senior claims. It rises with $D/S$ - more leverage concentrates more operating risk onto the residual rung. This is the market’s price for seniority: the more senior claims stacked above equity, the more equity must earn.

Coverage as the health of the senior claims. Interest coverage $\frac{\text{EBIT}}{\text{Interest}}$ and NetDebt/EBITDA measure whether the senior obligations can actually be serviced - the cash-flow test that precedes any liquidation test. A firm can be book-solvent (assets ≥ claims) yet cash-insolvent (can’t service the senior rungs), which is why coverage ratios, not just leverage ratios, matter (04 · Liquidity & Leverage).

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3. Computational Implementation - the liquidation waterfall, stdlib only

Runs on the standard library. A capital structure with $1,000$ of claims spread across the five rungs of the ladder is liquidated at five different asset values; we compute each claim’s recovery and confirm equity is the residual - paid last, often zero.

Read the ladder: senior debt is repaid in full whenever assets cover it ($A\ge 300$) and is the last claim to absorb losses, junior/mezzanine get hit as assets fall, and common equity gets nothing once liquidation drops below $700 - the sum of all senior claims. That is what “equity is the residual, riskiest claim” means numerically.

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4. Failure Modes & First-Principles Breakdowns

1. Assuming “debt is safer” is uniform across the ladder. Senior debt is safe; junior and mezzanine debt are much riskier - they are repaid only after senior claims, so their recovery falls earlier in a downturn. Treating all “debt” as equally protected ignores the entire point of the priority structure.
2. Reading book leverage without the ladder. A firm’s D/E and coverage ratios (Core Financial Ratios) say how much sits above equity, but not how senior that stack is. $100$ of senior debt and $100$ of subordinated debt impose very different risk on equity despite the same D/E.
3. Ignoring convertibles as both. A convertible is debt with a free option: it repays as debt but can convert into (diluting) equity if the stock rises. It sits between the pure debt rungs and equity - so it both dilutes existing holders (04 · Dilution) and carries equity’s downside. Graham & Dodd’s classic warning is that warrants/convertibles let a firm “siphon off” upside from common holders (see 04).
4. Conflating liquidation priority with going-concern return. The waterfall governs the terminal state. While the firm operates, seniority also shapes who gets paid first from operating cash flow (interest before dividends), which is the cash-flow layer that coverage ratios measure. A firm can rank high on the liquidation ladder yet still fail the cash test.
5. “Equity is wiped out in distress” ≠ “equity is worthless always.” Residual means subordinate, not valueless; in going-concern value, equity owns all upside above the senior stack. The risk is asymmetric, not uniformly bad - but the downside is total.

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5. References

• Modigliani & Miller, “The Cost of Capital…” (AER, 1958)
• Brealey, Myers & Allen, Principles of Corporate Finance
• Graham & Dodd, Security Analysis (6th ed.)
• Tirole, The Theory of Corporate Finance (2006)

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6. Connected Graph Bridges

• Back: 02 · Modigliani–Miller · Index Hub
• Forward: 04 · Dilution & Buybacks · 05 · Failure Modes
• Ratio layer: Core Financial Ratios - Liquidity & Leverage