Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in equation (36.3) with a = 0.05 and σ = 0.15. Construct a two-time-step tree for the price of wheat in a risk-neutral world.

A farmer has a project that involves an expenditure of $10,000 and a further expenditure of $90,000 in six months. It will increase wheat that is harvested and sold by 40,000 bushels in one year. What is the value of the project? Suppose that the farmer can abandon the project in six months and avoid paying the $90,000 cost at that time. What is the value of the abandonment option? Assume a risk-free rate of 5% with continuous compounding.