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. BrotGuts 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 25% (= 11/1.333, 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.

What is the initial cost (net outlay) today of investing in the replicating portfolio? (Round your answer to five decimal places.) a. $50.018 91 b. $50.014 14 c. $50.498 20 d. $54.175 82