Reciprocal or Mutual Holdings: Allocating Earnings and Selecting the Accounting Method.

Abstract The article presents a solution for allocating reciprocal earnings and a procedure for selecting an accounting method for the indirect and multiple ownership of firms. Preparing consolidated statements for complicated inter-ownership situations can be difficult. Thus, it is curious that the textbook presentations of allocating reciprocal earnings are, at best, incomplete and, at worst, conceptually wrong. That the final allocation adds to the same sum as the original set of earnings does not prove the correctness of the procedure. Perhaps the simplest explanation would be to describe the intermediate quantity for a given company as the net income that is reported on its income statement when it properly accounts for its investments in other corporations' securities. Each company's net income includes its own operating results counted several times--once as its own operating results and again as the investment income from other companies whose stock is mutually held. For both allocating earnings and choosing the right accounting method, the matrix-based procedures are straightforward conceptually, easy to prove correct and lead to an interpretation of the underlying problem when the procedures are initially inoperable for allocating earnings.