Final answer:
The task not performed by the transfer agent is Setting the Declaration Date, which is the responsibility of the company's board of directors.
Step-by-step explanation:
The function that is not a part of the transfer agent's responsibilities is C. Setting the Declaration Date. The declaration date is set by the company's board of directors and is the date on which the board announces the forthcoming dividend payment. In contrast, transfer agents have multiple roles including A. Mailing dividend payments to shareholders, B. Preparing and mailing proxies, and D. Canceling old shares and issuing new shares. Transfer agents ensure that shareholders receive their dividends in a timely manner and also handle proxy materials for corporate votes. Furthermore, they maintain records of shareholder accounts and oversee the issuance of stock certificates.