According to the Merton model, the value of a firm's equity is influenced by the volatility of firm value. Generally, as the volatility of the firm's value increases, the value of the equity increases relative to the value of the debt. Conversely, a lower volatility of firm value leads to a lower value of equity compared to the debt. This relationship is attributed to the fact that increased volatility increases the likelihood of the firm's value falling below the value of its debt, resulting in a higher probability of default. As a result, the equity holders face a higher risk of significant loss and, therefore, their claims become relatively less valuable compared to the debt holders.

A is incorrect because the value of a firm's equity is not equal to the value of its debt in the Merton model.
B is incorrect because the value of a firm's equity can be either higher or lower than the value of its debt depending on the volatility of firm value.
C is incorrect because the value of a firm's equity can be either higher or lower than the value of its debt depending on the volatility of firm value.

Things to Remember

• Increased volatility of firm value leads to a higher value of equity relative to the debt.
• Lower volatility of firm value leads to a lower value of equity relative to the debt.
• The Merton model considers the probability of default based on the firm's value and the volatility of that value.