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 optimizing under the per-tier rental-rate budget yields the closed-form rule \ (wₜ^* (r) = ₜ / (ₜ + r) \) and the comparative static \ (w₆^*/ r > 0\). Four propositions link pre-deal surface-tier intensity, governance horizon, cost-of-capital shocks, and capability-rotation stage to M, ) = ₜ / ₜ (ₜ^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.