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Vd2 An entrepreneur finances her project with equity (that is owned by the entrepreneur) and debt (that matures in three years)

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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 ?", the equity value at time t as ?", and the debt value at time t as ?". Let today be time t=0, and three years from now be time t=T=3.

a. Draw the plot of ?t against ?t, and the plot of ?t against ?t, respectively. (Recall that T is equal to 3, the date of maturity of the debt).

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.

c. Suppose the value of her assets ?t 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., ?0 = $100 million), use the Black-Scholes formula to calculate the value of her equity today (i.e., what is ?0?)