Please provide typed answer, with clear step-by-step calculations and explanations. Any assumptions made must be stated. Please make sure to clearly mark the final answer.

Suppose the price of gasoline per gallon is currently $5. The risk manager of Universe Airlines expects the price per gallon next year to be either $7 or $4 with equal probabilities. The company plans to buy 1 million gallons of gasoline in one year. The risk manager is concerned about future rising cost of gasoline and is considering using either futures or calls to hedge against the risk. Suppose the riskfree interest rate is 10% per annum.

a) What is the futures price of gasoline per gallon for delivery in one year?

b) What are the possible payoffs of the futures one year from now?

c) If calls are used, only the ones with the same exercise price as the futures price are available now. How much would it cost to buy the calls? What are the possible profits of the calls (the payoffs net of the call premium) one year from now?

d) Suppose the investors of the company are risk averse and their collective risk attitude can be described by log utility. Assume that the risk manager maximizes the expected utility of the company which is worth $20 million right now. Which hedging method is better, the futures or the calls?