When international accounting standards were renamed to become international financial reporting standards, this seemed to imply that accounting no longer needed to exist, but rather had to be reconsidered as a part of financial communication and advertising. Does traditional accountability no longer matter? Betrayed investors and globalized stakeholders would dissent. A difference of nature continues to exist between fair values disclosed by managers and certified by auditors, and the actual performance generated by the enterprise entity through time, space, and interaction. In a world shaped by complex organizations facing unfolding changes, hazard and limited knowledge, the quest for fundamental principles of accounting is not academic. Accounting principles constitute a primary way that the creation and allocation of business incomes is governed; that is, fairly managed and regulated in the public interest, having respect to “other people interests.” This article adopts a dualistic posture that opposes the accounting conceptual frameworks based on fair value (market basis) and historical cost and revenue (process basis). The fundamental premises about the underlying economics of the enterprise entity are discussed, including the representation of the business and the concepts of asset and liability. References are made to the case of accounting for intangibles, and to the distinction between equities and liabilities. The cost and revenue accounting perspective is then defended in terms of accountability, but also from the informational viewpoint: historical accounting information plays a special role as a lighthouse in the dynamic and strategic setting of the Share Exchange. In particular, two refinements of the historical cost (and revenue) accounting model are suggested. The first one regards the treatment of earned revenues from continuing operations, and the second, the recognition of shareholders' equity interest computed on the actual funds provided in the past, coupled with the distinction between shareholders' equity and entity equity.