A company has production of 500 kilograms of aluminum and a face value of debt of40 000 due in one-year. If its cash flows next year drop below the face value of debt,then the company will default. The price of aluminum is currently 100 per kilogram.You can assume the returns on the price of aluminum are normally distributed, withan expected return of 0% and an annualized volatility of 20%+X%, where X is the 4thdigit of your student ID (e.g., if the 4th digit is 5, then the volatility would be 25%)

(a) Estimate the probability the company will default given the above information.Explain your result and what you are assuming?

(b) You observe that historically companies in a similar position, had a default probability of 12%. Explain why your result from part (a) might differ from the historical probability?

(c) Suppose that if the company defaults, then it face distress costs of 10 000, but that it would cost 0.50 per future in transaction costs to hedge its production. Discuss how the company should find its optimal hedge, being specific about what pieces the calculation would involve. You do not need to solve for the optimal hedge.