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 equity as a call option on the firm's assets, with the strike price being the face value of the debt. Given the parameters, the correct answer requires solving for the asset volatility that makes the model's equity value equal to the given equity value. This involves complex calculations not provided in the question, but the correct answer is typically found using numerical methods or formulas derived from the Merton model.

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