Suppose the current value of a firm's assets is $100 million,and the value of equity in the firm is $40 million.Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years,and a face value of $70 million.Finally,suppose that the risk-free rate of interest is 4% (continuously-compounded terms)for all maturities.Assuming that firm value evolves according to a lognormal diffusion (as in Merton,1974),what is the volatility of the firm's assets?
A)10.0%
B)19.2%
C)24.2%
D)35.4%

Question

Quizplus · Accepted Answer

The volatility of the firm's assets can be derived using the Merton model, which links the value of the firm's equity, the value of its debt, the risk-free rate, and the volatility of the firm's assets. Given the information, the correct answer involves applying the Merton model formulas, which require complex calculations not directly provided in the question. However, the correct choice, based on the Merton model's application to the given values, is 19.2%.

Suppose the Current Value of a Firm's Assets Is $100