Which statement describes the relationship between risk and the cost of equity?

The correct choice reflects a fundamental principle in finance: there is a direct relationship between risk and the cost of equity. Higher risk typically implies that investors require a greater return to compensate for the additional uncertainty associated with investing in a particular equity. This is based on the risk-return tradeoff, which posits that to attract investors, companies must offer higher potential returns on investments that carry more risk.

In the context of equity financing, if a company is perceived as risky (perhaps because of volatile earnings, economic uncertainty, or operating in a highly competitive industry), investors will expect a higher rate of return to justify the risk they are taking on by purchasing the company's stock. Hence, as the perceived risk increases, the cost of equity rises correspondingly to reflect the higher expected returns demanded by investors.

This understanding is crucial for businesses when determining their capital structure and financing strategies. It helps them assess how changes in their operational risk profile might impact their cost of capital and ultimately their investment decisions.