Why do two firms with identical revenues, margins, and aggregate investment generate exit multiples of 2× versus 9× revenue and divergent post-acquisition performance? Capital allocation theory, dynamic capabilities, and marketing-finance literatures have each left the direction of investment within a business implicit. This paper formalizes the cross-tier allocation problem using a vector w spanning five operating tiers that differ in asset durability. Each tier accumulates stock according to a differential equation with tier-specific decay rates δt ranging from. 50/year at the organizational surface (Tier 6: advertising, paid media) to. 05-. 10/year at foundational layers (Tiers 2-3: business-model architecture, legal position). Long-run value is a discounted Cobb-Douglas aggregator incorporating Jorgensonian user costs (δt + r) and ownership-separability weights. Optimizing subject to the per-tier rental-rate budget constraint yields the closed-form rule wₜ (r) = αt / (δt + r) and the comparative static ∂w₆/∂r > 0: higher discount rates increase optimal allocation to the high-decay surface tier at the expense of durable substrate. Four propositions follow: pre-deal surface-tier intensity predicts post-acquisition goodwill impairment; long-horizon governance lowers equilibrium surface-tier share; cost-of-capital shocks shift allocation predictably; and capability-rotation stage moderates returns to codification investment. The framework supplies a missing architectural mechanism that integrates resource-based, dynamic-capability, and internal-capital-market streams, making investment direction – not merely intensity – a consequential strategic choice. Includes paper. yaml (Paper Spec v0. 1. 0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. See https: //github. com/spectralbranding/paper-spec for the standard.
Dmitry Zharnikov (Thu,) studied this question.