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Penman’s Perspective

Penman’s Accounting for Value uses residual income valuation (RIV):

$$ V_0 = B_0 + \sum_{t=1}^\infty \frac{\text{ROE}t - r_e}{r_e} \cdot B{t-1} $$

  • $ B_0 $: Book value,
  • $ \text{ROE}_t $: Return on equity,
  • $ r_e $: Cost of equity.

Why No $ d $?

  • Penman focuses on accounting residuals (earnings above required return on equity), not cash flows or annuities like our model.
  • Dividends ($ f_d $) are implicit in book value growth ($ B_t = B_{t-1} + \text{Earnings}_t - \text{Dividends}_t $), so he avoids explicit $ f_d $ terms.
  • Dilution ($ d $) is embedded in diluted EPS and book value per share—he assumes financial statements (via diluted shares) capture it, not requiring a separate $ g - d $ adjustment.
  • Critique: His empirical work (e.g., Penman & Zhu, 2014) tests RIV on broad samples, but doesn’t isolate $ d $’s effect across firms—our concern about lack of company-specific research is valid.

Damodaran’s Perspective

Damodaran’s DCF:

$$ V_0 = \sum_{t=1}^T \frac{\text{FCFF}_t}{(1 + WACC)^t} + \frac{\text{Terminal Value}}{(1 + WACC)^T} $$

  • $ \text{FCFF} $: Free cash flow to firm (pre-dilution),
  • $ WACC $: Weighted average cost of capital,
  • Terminal: $ \frac{\text{FCFF}_{T+1}}{WACC - g} $.

Why No $ d $?

  • $ g $: Perpetual growth rate (revenue or earnings), adjusted for reinvestment, not explicitly net of dilution.
  • SBC: Added back to FCFF as non-cash (e.g., in his AMZN valuations), with dilution in diluted shares for equity value per share.
  • Approach: In The Dark Side of Valuation, he models growth firms (e.g., AMZN) with high SBC, but $ d $ is implicit in share counts, not a standalone $ g - d $ term.
  • Critique: His case studies (e.g., Tesla, GOOGL) don’t test $ d $’s standalone impact across a broad sample—our push for generalization finds less echo here.

Why $ d $ Is Overlooked

  • Accounting Focus: Penman and Damodaran rely on diluted shares to bake in dilution, assuming $ d $’s effect is in EPS or cash flow adjustments.
  • Growth Bias: Valuation prioritizes $ g $ (top-line or bottom-line growth), treating $ d $ as a secondary adjustment via share counts.
  • Data Rarity: Historical $ d $ (like our 10-year averages) isn’t standard in datasets—researchers lean on SBC or buyback flows.

The originality of our approach stems from blending Mauboussin’s probabilistic lens (metrics for all firms) with a unique $ d $-driven tweak—most stick to $ g $ and dividends without explicit share dynamics.

Who Else Values $ d $?

Here are other valuation frameworks where $ d $ gets traction:

  1. Mauboussin’s Extensions:

  2. In Expectations Investing (2021), Mauboussin adjusts cash flows for share issuance/buybacks implicitly via diluted shares and SBC add-backs, akin to our $ d $ in $ r $. He doesn’t isolate $ d $, but his focus on firm-specific drivers (e.g., “value factors”) aligns with our generalization goal.

  3. Relevance: He’d likely support $ d $ if framed as a probabilistic metric—e.g., AMZN’s 1.25% headwind vs. GOOGL’s -0.93% tailwind.

  4. Bradford Cornell (UCLA):

  5. Known for The Equity Risk Premium, Cornell’s valuation work (e.g., Cornell & Damodaran, 2020) adjusts growth for firm-specific risks. While not explicit on $ d $, his emphasis on long-term share dynamics (e.g., buybacks in tech) parallels our sticky $ d $.

  6. Relevance: He might advocate averaging $ d $ over 10 years as a structural factor.

  7. Aswath Damodaran (Implicitly):

  8. In his “Dark Pool” adjustments (e.g., valuing young firms), he nets SBC into FCFF and uses diluted shares, indirectly capturing $ d $. Our explicit $ g - d $ could be seen as an extension—Damodaran’s silence on $ d $ might just be convention, not rejection.

  9. Practitioners (e.g., Warren Buffett):

  10. Buffett’s owner earnings (net income + non-cash - maintenance capex) add back SBC, while his focus on per-share value growth implicitly nets out dilution. Our $ d $ in $ r $ echoes this—e.g., AMZN’s 1.25% dilutes per-share value over time.

  11. Research Niche:

  12. Fama & French (2018): Their 5-factor model indirectly ties dilution to profitability and investment—firms with high $ d $ (like AMZN) might underperform if growth doesn’t offset.

  13. McLean & Pontiff (2016): Post-publication studies show dilution-heavy firms (e.g., tech) face valuation penalties—our $ d $ could generalize this.

Our Approach vs. Tradition

  • Penman: Avoids $ d $ in RIV, trusting diluted EPS—our annuity + $ d $ diverges, emphasizing cash flow timing.
  • Damodaran: Subsumes $ d $ in diluted shares and FCFF—our $ g - d $ makes it explicit, risking overlap but adding granularity.
  • Our: $ d $ as a first-order driver (like $ g $, $ f_d $) aligns with Mauboussin’s firm-specific metrics, generalizing across AMZN (+1.25%) to AAPL (-4.62%).

Why we are Unique: we are not bending to market price (e.g., AMZN’s $2.3T cap) but testing intrinsic value with $ d $ as a structural habit—Penman and Damodaran prioritize accounting or cash flow purity over share dynamics.

Validation with our Data

  • AMZN: $ d = 1.25\% $, SBC 2.69%, srpd 4.01%—dilution cost exceeds SBC, supporting $ d $’s role.
  • GOOGL: $ d = -0.93\% $, SBC 6.82%, srpd -5.29%—buybacks flip $ d $, reducing valuation drag.
  • Across Firms: NVDA’s $ d = 1.06\% $, AAPL’s -4.62%—policy-driven $ d $ varies widely, justifying its inclusion.

Fellow Travelers

consider:

  • Mauboussin: Generalize his “value drivers” with $ d $ as a metric—our 10-year average fits his probabilistic ethos.
  • Buffett-Inspired Analysts: Per-share focus (e.g., Morningstar’s intrinsic value) often nets dilution implicitly—our explicit $ d $ formalizes it.
  • practitioner Blogs: Less academic, but some (e.g., Seeking Alpha contributors) stress $ d $ for tech valuations.