Liu Industries is a highly levered firm. Suppose there is a large probability that Liu will default on its debt. The value of Liu’s operations is $4 million. The firm’s debt consists of 1-year, zero coupon bonds with a face value of $2 million. Liu’s volatility, σ, is 0.60, and the risk-free rate rRF is 6%.

Because Liu’s debt is risky, its equity is like a call option and can be valued with the Black-Scholes Option Pricing Model (OPM). (See Chapter 8 for details of the OPM.)

(1) What are the values of Liu’s stock and debt? What is the yield on the debt?

(2) What are the values of Liu’s stock and debt for volatilities of 0.40 and 0.80? What are yields on the debt?

(3) What incentives might the manager of Liu have if she understands the relationship between equity value and volatility? What might debtholders do in response?