Final answer:
The correct answer is "Investments accounted for using the cash method" which is not a recognized practice for reporting intercorporate equity investments. The recognized methods are equity method, fair value method, and cost method.
Step-by-step explanation:
The category that is not one of the reporting categories for intercorporate equity investments is Investments accounted for using the cash method. There are three primary methods for accounting intercorporate investments: equity method, fair value method (also known as the market value method), and cost method. The cash method is not a recognized accounting practice for this type of investment. When a company holds a significant influence over an investee (usually indicated by a 20-50% ownership stake), the equity method is used, whereby the investor records its share of the investee's net income or loss. If the investment grants the investor less influence, typically when owning less than 20%, the fair value method might be applied, where the investment is reported at current market value, with changes recognized in earnings. For investments that do not grant significant influence and also do not provide readily determinable fair values, the cost method may be applied, where the investment is recorded at historical cost.