Final answer:
Texas Corporation's acquisition of additional shares and consequent significant control over Arkansas Corporation is a change in accounting principle requiring prospective adjustment, transitioning from the cost method to the equity method of accounting. Option C is correct.
Step-by-step explanation:
The change described in the scenario where Texas Corporation initially purchased a 15% interest in Arkansas Corporation and later acquired an additional 20% share, with Texas Corporation's President becoming a member of Arkansas Corporation's board of directors, is considered a change in accounting principle that requires prospective adjustment.
Since the investment now provides Texas Corporation with significant influence over Arkansas, this change reflects a transition from the cost method of accounting to the equity method of accounting. This accounting principle change is handled prospectively because the new method is applied to future financial statements from the date of change, and past financial statements are not revised.