Final answer:
A conflict of interest with an existing client is the most likely factor to cause a CPA to decline a new audit engagement.
Step-by-step explanation:
A conflict of interest with an existing client is the factor that is most likely to cause a CPA to decide not to accept a new audit engagement. When a CPA has an existing client that has a conflict of interest with the potential new client, it can compromise their independence and objectivity in performing the audit.
For example, if a CPA is auditing a company and discovers that the company has engaged in fraudulent activities, they may have to report this to the appropriate authorities. However, if the CPA also has a financial relationship with the same company or its management, it can create a conflict of interest that may prevent them from taking appropriate action.