Where to Invest Within the Firm: Organizational Tiers, Discount Rates, and AI Penetration
Year: 2026
Type: preprint
Abstract: 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 δt 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 (δt + r); optimizing under the per-tier rental-rate budget yields the closed-form rule wt*(r) = αt / (δt + 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&A outcomes. The framework then adds two AI-specific shocks per tier – a cost shock γt and a durability shock Δt – yielding the generalized rule wt*(r; γ, Δ) = αt / [γt · (δteff + 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 github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.
Author: Zharnikov, Dmitry
Language: English
Subfield: Strategy and Management
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7160644103