Final answer:
The factor related to client acceptance that is affected by the firm's ability to perform services and meet client needs is Competence, which ensures the audit team is qualified to carry out the audit effectively.
Step-by-step explanation:
The question pertains to the client acceptance phase of an audit, focusing specifically on factors that auditors must consider when deciding whether to accept a new audit client. In this scenario, the factor affected by determining that the firm has the expertise to perform the services and can meet the client's needs is Competence. Competence refers to the audit firm's ability to perform the audit engagement, having the necessary skills and knowledge. This does not directly impact Independence, which relates to the unbiased stance of the auditors; Integrity of management, which deals with the honesty and ethical behavior of the client's management; or Special circumstances and unusual risks, which covers the risk factors associated with the audit, but rather, it ensures that the audit team is qualified to carry out the audit effectively.