Which of the following is an example of an external threat to a company's profitability?

The correct answer is a potential hostile takeover, as it represents a significant external threat that can impact a company's profitability. A hostile takeover occurs when an acquiring company attempts to take control of a target company against its will, and this can lead to instability within the organization, loss of key personnel, or shifts in strategic direction. Such changes can adversely affect profitability, shareholder confidence, and overall market performance.

In contrast, the other options reflect internal factors rather than external threats. The lack of a distinctive competence is an internal weakness that may hinder a company's competitive position but is not an external threat. High production costs, while they can impact profitability, are influenced by internal operational decisions and not necessarily by external factors. A strong brand image is a valuable internal asset that can enhance profitability rather than pose a threat to it. Therefore, the potential for a hostile takeover stands out as an external factor that can directly threaten a company's financial health.