Where to Invest Within the Firm: Organizational Tiers, Discount Rates, and AI Penetration

Why do two firms with identical revenues, margins, and aggregate investment generate exit multiples of 2× versus 9× – and why do identical AI investments produce divergent M&A multiples despite comparable short-run gains? This paper formalizes cross-tier allocation using a vector w over operating tiers differing in asset durability, with decay rates δ_t ranging from .50/year at the organizational surface (advertising) to .05–.10/year at foundational layers. Long-run value is a discounted Cobb-Douglas aggregator with Jorgensonian user costs \((\delta_t + r)\); optimizing under the per-tier rental-rate budget yields the closed-form rule \(w_t^*(r) = \alpha_t / (\delta_t + r)\) and the comparative static \(\partial w_6^*/\partial r > 0\). Four propositions link pre-deal surface-tier intensity, governance horizon, cost-of-capital shocks, and capability-rotation stage to M&A outcomes. The framework then adds two AI-specific shocks per tier – a cost shock \(\gamma_t\) and a durability shock \(\Delta_t\) – yielding the generalized rule \(w_t^*(r; \gamma, \Delta) = \alpha_t / [\gamma_t \cdot (\delta_t^{\text{eff}} + r)]\) and three further propositions: surface-tier AI raises short-run earnings yet lowers long-run multiples; a discrete substrate-building threshold exists at Tier 4; and AI's net value effect flips sign with the principal's effective discount rate. Investment direction, not intensity, is the consequential strategic choice. Includes zharnikov-2026aj-tier-allocation.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. The paper's full machine-first bundle (the SPINE claim/dependency graph and the ONTOLOGY term module) lives in the public repository; see https://github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.