Problem 2. (Equity and debt as options, 15') An entrepreneur finances her project with equity (that is owned by the entrepreneur) and debt (that matures in three years). She is supposed to repay $80 million for her debt in three years. If the total assets of her project turn out to be valued above $80 million three years from now, then she will liquidate her assets, repay $80 million in full, and retains the rest as her equity. However, if her total assets turn out to be valued lower than $80 million three years from now, then due to limited liability, she does not need to repay $80 million in full. In that case, she will liquidate everything she has, pay off the creditor with whatever her assets are worth (which is less than $80 million), and retain nothing in three years. Let the value of the total assets at time t be denoted as St, the equity value at time t as Et, and the debt value at time t as Dt. Let today be time t=0, and three years from now be time t=T=3. a. Draw the plot of ET against ST, and the plot of DT against ST, respectively. (Recall that T is equal to 3 , the date of maturity of the debt) (8') b. Economists say that, with limited liability, corporate equity has features of a long call option on corporate assets, and corporate debt has features of a short put on corporate assets and a long bond. Briefly explain why that makes sense with your results from part a. (3') 1 c. Suppose the value of her assets St satisfies the Black-Scholes assumptions for the underlying asset price. The continuously compounded risk-free rate is 4%. The volatility of the return on her assets is 30%. Do not consider any form of dividend payouts. If her assets are worth $100 million today (i.e., S0=$100 million), use the Black-Scholes formula to calculate the value of her equity today (i.e., what is E0 ?) (4') Problem 2. (Equity and debt as options, 15') An entrepreneur finances her project with equity (that is owned by the entrepreneur) and debt (that matures in three years). She is supposed to repay $80 million for her debt in three years. If the total assets of her project turn out to be valued above $80 million three years from now, then she will liquidate her assets, repay $80 million in full, and retains the rest as her equity. However, if her total assets turn out to be valued lower than $80 million three years from now, then due to limited liability, she does not need to repay $80 million in full. In that case, she will liquidate everything she has, pay off the creditor with whatever her assets are worth (which is less than $80 million), and retain nothing in three years. Let the value of the total assets at time t be denoted as St, the equity value at time t as Et, and the debt value at time t as Dt. Let today be time t=0, and three years from now be time t=T=3. a. Draw the plot of ET against ST, and the plot of DT against ST, respectively. (Recall that T is equal to 3 , the date of maturity of the debt) (8') b. Economists say that, with limited liability, corporate equity has features of a long call option on corporate assets, and corporate debt has features of a short put on corporate assets and a long bond. Briefly explain why that makes sense with your results from part a. (3') 1 c. Suppose the value of her assets St satisfies the Black-Scholes assumptions for the underlying asset price. The continuously compounded risk-free rate is 4%. The volatility of the return on her assets is 30%. Do not consider any form of dividend payouts. If her assets are worth $100 million today (i.e., S0=$100 million), use the Black-Scholes formula to calculate the value of her equity today (i.e., what is E0 ?) (4')