PetroWorld is an international conglomerate with a petroleum division and is currently competing in an auction to win the right to drill for crude oil on a large piece of land in one year the current market price of crude oil is $50 per barrel and the land is believed to contain 800,000 barrels of oil. If found the oil would cost $55 million to extract. U.S. treasury bills that mature in one year yield a continuously compounded interest rate of .6 percent. The standard deviation of the returns on the price of crude oil is 85 percent. Use the black-scholars-merton model to calculate the maximum bid that the company would be willing to make at the auction.

Suppose instead that the available oil reserves follows a lognormal distribution with a mean of 800,000 barrels and standard deviation of 300,000 barrels the extraction cost also falls a longnormal distribution with a mean of $55 million and standard deviation of $35 million. Considering the current economic conditions, the federal reserve is likely to raise interest rate soon, which could change the yield on the one-year U.S. treasury bills to range between 1.25 percent to 2.25 percent (uniformly distributed). What is, on average, the maximum bid that the company would be willing to make? Use the black-Scholes-Merton model.Show all formulas, steps and work.

If possible please show all your work in excel.