BrotGut, a bakery chain which bakes and distributes bread to the Sydney market, is concerned about the impact of the war in the Ukraine on its manufacturing costs. BrotGut is worried that the price of wheat could rise sharply. As a result of its concerns, BrotGut is considering entering into a European call option contract with a strike price of $420 per metric tonne. BrotGut's financial modelling team have studied wheat prices and have come to the conclusion that over the next three months the price of wheat could rise by a third if the war in the Ukraine continues (occurring with probability p = 0.95) or fall by j (= 1 − 1/1.333, occuring with probability ˙ 1 − p = 0.05) if the war ends. The current price per metric tonne of wheat is $400. BrotGut can borrow money today for any period under six months at a rate of j12 = 4% p.a.

a. Use the contingent payments method to find the amount BrotGut would be willing to pay today (i.e., the option premium) for the call option. Round your answer to five decimal places. Include in your answer a carefully labelled contingent cash flow diagram that illustrates your modelling approach.

b.  Consider the replicating portfolio (that is, the investment strategy which will give identical payoffs, at the end of three months, to the call option contract) that involves buying h metric tonnes of wheat today, and borrowing $B for three months. Illustrate this model in a carefully labelled contingent cash flow diagram. Find the values of h and B (round your answers to five decimal places).

c. What is the initial cost (net outlay) today of investing in the replicating portfolio? (Round your answer to five decimal places.)