Final answer:
The event that requires recognition in the auditor's opinion for consistency is the change from the cost method to the equity method of accounting for investments in common stock, as it is a significant change in accounting principle.
Step-by-step explanation:
The student is asking about the scenarios requiring recognition in the auditor's opinion regarding consistency in financial reporting. Among the options provided, the event requiring recognition would be: the change from the cost method to the equity method of accounting for investments in common stock. This is because such a change represents a change in accounting principle, and the auditor must evaluate whether the change has been properly accounted for and adequately presented and disclosed in the financial statements.The correction of an error due to a mathematical mistake, a change in estimate for warranty costs, and a change in depreciation method that does not impact the current year's financials are generally not considered changes in accounting principle that require disclosure for consistency. However, significant errors corrected in prior periods could potentially require disclosure depending on their nature and impact on the financial statements.
Consistency in financial reporting is important as it allows for comparability over time. The coherence theory of truth implies that for statements to be true, they must consistently fit within a wider system of beliefs. Ultimately, the first judgments or statements need to be verified directly to establish a basis for coherence.The item that requires recognition in the auditor's opinion as to consistency is option 3, which is the change from the cost method to the equity method of accounting for investments in common stock.This type of change in accounting method impacts the comparability of financial statements over time, and therefore requires explicit recognition by the auditor.Options 1, 2, and 4 do not require recognition as to consistency because they do not involve changes in accounting principles or methods that would affect the comparability of financial statements across periods.