A.2.3 Valuation Multiples

Basic Prerequisites: 01 · From Zero and Equity Valuation.

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1. Intuition & Practical Objective

Valuation multiples are ratios where the numerator is a price - “what is the market paying per unit of this fundamental?” They convert a statement fundamental (earnings, book value, EBITDA, cash flow) into a relative-price language that lets you compare otherwise incomparable firms. Their power is comparison: is this firm cheaper or dearer than its sector, its history, its own growth? (Fama–French 1992 made the case that two of them - P/B and P/E - are not just descriptors but priced characteristics: low-P/B, high-E/P firms earned higher average returns.)

The two families matter because they answer different questions:

• Equity multiples (P/E, P/B, earnings yield, FCF yield) divide equity market value by an equity fundamental. They price what the shareholder owns.
• Enterprise multiples (EV/EBITDA) divide enterprise value - equity plus net debt, i.e. the whole operating business - by a pre-financing fundamental. They price the whole firm, ignoring how it is financed.

A firm with heavy debt has a low P/E but a normal EV/EBITDA, because P/E ignores the debt that EV captures. That single distinction is why EV/EBITDA exists: it lets you compare firms with different capital structures on the operating business alone (Pinto et al., the CFA standard, is the canonical treatment of this layer).

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2. Mathematical Ground Truth & Derivations

Notation. MV market value of equity, BVE book value of equity, NI net income, NetDebt $=$ TotalDebt $-$ Cash, EBITDA $=$ EBIT $+$ D&A, FCF free cash flow, EV $=$ MV $+$ NetDebt.

$$\text{P/E}=\frac{\text{MV}}{\text{NI}},\text{Earnings yield}=\frac{\text{NI}}{\text{MV}}=\frac{1}{\text{P/E}},\text{FCF yield}=\frac{\text{FCF}}{\text{MV}},$$ $$\text{P/B}=\frac{\text{MV}}{\text{BVE}},\text{EV/EBITDA}=\frac{\text{MV}+\text{NetDebt}}{\text{EBITDA}}.$$

The inverse-yield identity. P/E and earnings yield are reciprocals by construction: $\text{Earnings yield}\equiv \frac{1}{\text{P/E}}$. This is not an empirical finding - it is a definitional identity (and the machine-verification §3 checks it). Framing the same number as “a multiple of 17.1” vs. “a yield of 5.8%” changes the intuition, not the data.

Why EV/EBITDA is the capital-structure-neutral multiple. Note

$$\text{EV}=\text{MV}+\text{NetDebt}=\text{MV}+(\text{TD}-\text{Cash}),$$

so the denominator must be a pre-interest (pre-financing) cash-flow proxy - EBITDA - for the ratio to be internally consistent. Matching an equity numerator with an enterprise denominator, or vice-versa, is a category error (see Failure Modes #1).

The Penman anchor on P/B (Ch 2, 6). Price-to-book is the ratio that asks “how much value is the market seeing beyond the book?” Because book value is the accounting capital that the residual-income view says anchors intrinsic value, a P/B > 1 means the market is paying for future residual income (value creation above the required return); P/B < 1 is the classic Graham bargain where price sits below accounting capital.

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3. Computational Implementation - multiples, the yield identity, and a debt-sensitivity check

Stdlib only. Computes the equity and enterprise multiples for the sample firm, verifies P/E × EarningsYield = 1, and demonstrates the capital-structure point by showing how much EV/EBITDA does not move when leverage does (unlike P/E).

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4. Failure Modes & First-Principles Breakdowns

1. Matching error: equity vs. enterprise. Dividing EV by net income, or MV by EBITDA, is a category error - the numerator and denominator measure different claimants. The ratio is only meaningful when both sides are equity (P/E, P/B, yields) or both are enterprise (EV/EBITDA).
2. Negative or near-zero denominators. A firm with losses has no meaningful P/E (negative earnings make the “multiple” meaningless, not cheap); FCF yield likewise breaks for negative FCF. The standard response is to switch lenses - to EV/Sales or to a cash-flow-anchored measure - or to the distress toolkit in 06 · Advanced Extensions.
3. P/E conflates the whole capital structure and the business. For a levered firm P/E reflects both operating quality and financing. EV/EBITDA strips the financing out - use it (with its sector-relative caveats) when comparing firms of different leverage.
4. Cross-sectional blindness again. P/E and P/B are sector- and growth-dependent by design (a high-growth firm legitimately carries high P/B). Fama–French 1992’s own result is a cross-sectional ordering - apply these multiples within comparable groups, never as universal cutoffs.
5. GAAP vs. adjusted earnings. EBITDA and “adjusted EPS” are non-GAAP; they exclude items real cash will someday hit. A multiple on an aggressive adjusted number overstates cheapness - always check what was stripped out (ties into Accounting Quality & Red Flags).

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5. References

• Pinto, Henry, Robinson & Stowe (CFA), Equity Asset Valuation
• Damodaran, Investment Valuation
• Penman, Financial Statement Analysis and Security Valuation
• Fama & French, “The Cross-Section of Expected Stock Returns” (JF, 1992)
• Campbell & Shiller, “Valuation Ratios and the Long-Run Stock Market Outlook” (JPM, 1998)

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6. Connected Graph Bridges

• Back: 02 · Profitability Ratios · Index Hub
• Forward: 05 · Failure Modes · Equity Valuation - DCF & Comps
• Base: Financial Statement Analysis