4. Exendine Oil, an exploration and development company located in Okesa, Oklahoma plans to bid for a one-year option to horizontally drill and fracture the old Drummond oil field. The option gives Exendine the right to drill the well anytime during the next year. The option expires at the end of one year if the firm fails to begin drilling. The total costs of drilling and fracturing the well would be $3.10 million. The well is certain to produce 20,000 barrels of oil per year for three years before oil ceases to flow into the lateral sections of the well. The price of oil, which is currently $56 dollars per barrel, follows a binomial process such that over the next six months the price will either increase to $70 per barrel or decrease to $44.80 per barrel. If the price of oil increases to $70 per barrel then over the following six months the price of oil will either increase to $87.50 or decrease back to $56 per barrel. If the price of oil initially falls to $44.80, over the following six months the price will either increase to $56 per barrel or decrease to $35.84 per barrel. If Exendine decides to drill at the end of the year (at the option expiration), the firm would be able to lock-in the selling price for production from the well by entering into a fixed-price supply contract to sell the yearly production from well at the end of year 1 market price of oil ($35.84, $56 or $87.50), with delivery of the first years production to occur one year after the well is drilled (at the end of year 2). Assuming that Exendine Oil has a required yearly return of 9.5 percent and that the continuously compounded risk-free rate of interest is 1.395 percent per year (.01395), determine the maximum amount that Exendine Oil should pay for the option to drill in the Drummond oil field.