Consider a firm that has assets worth $1,000,000 today. It has a single zero-coupon debt issue with face value $800,000 and a time-to-maturity of five years. At the time of debt maturity, the firm will liquidate its assets, pay debt holders the face value (if possible), and pay equity holders the residual. The asset volatility (?v) of the firm is 20% and the risk-free rate is 2%
1. What is the risk-neutral probability that the firm will survive to T = 5?
2. What is the value of debt in the firm? What is the value of equity?
3. Suppose that the value of the firm increases to $1,200,000. What is the value of debt in the firm? What about equity? Do equity holders, debt holders, or both benefits?
4. Suppose that we revert back to the firm value and parameters used in (1) and (2) except that the underlying asset volatility increases to 30%. What is the value of debt? What about equity? Does an increase in asset volatility benefit equity holders or debt holders?