Violations of the Standard NPV Rule, Dividend and Capital Structure Relevance, and Limited Arbitrage with Differential Discounting

Analysis of a related set of models of capital investment in which an owner (principal) hires a manager (agent) to oversee production is provided. Five models reflect variation from simple to complex and, in a different ordering, from less to more realism. The key assumption driving results is that the agent discounts future consumption more than the principal. A naïve measure of NPV is based on equal discounting. This benchmark is compared to the principal's investment decisions based on the effects of differential discounting on agent compensation. Agent compensation is shifted forward as much as possible, taking advantage of differential discounting. Other important assumptions, varied throughout the analysis, are: (1) whether the principal is financially constrained (no borrowing) or whether unlimited access to borrowing is available, and (2) whether agent compensation is unconstrained, or whether there is a lower bound on compensation. Three main results are illustrated: (A) violations of the naïve standard zero-NPV Rule, (B) dividend relevancy, and (C) arbitrage profits. All of these effects disappear with equal discounting. The first four models formed by the variations in (1) and (2) produce these effects, but never all at once. The final model, with costly borrowing, where the borrowing rate of interest exceeds the owner's savings (discount) rate, provides for an explanation of standard NPV Rule violations, dividend relevance, limited arbitrage, and capital structure relevance simultaneously