You are considering biding on the right to extract crude from a patch of land to hold a large reservoir of crude. Current price of crude is $45 per barrel. You know crude prices fluctuate but you have no particular insight into what prices will be in the future. However, you do know that the annual standard deviation of returns for crude is 30% or 0.30. The bidding rights are for one year. It costs $50 per barrel to extract crude. You are trying to determine the maximum amount that you can rationally bid per barrel of drilling rights.

a) Show the static NPV Framework for evaluating this problem. What would you bid under this approach? Is this a satisfactory answer?

b) Now set this up as a real options problem: for this situation, define the following: the underlying asset, the option exercise price, the option premium (the price you pay to buy the option).

c) Apply the Black and Scholes model to determine the maximum amount you can bid. The risk free rate is 4% annual.

d) Now work out the binomial solution of this problem. Use 2 steps, that is each step is 6 months. Compare the answers you get for the Black and Scholes and the Binomial models and comment on any difference.