Poppy Popcorn is a company that produces popcorn balls for Halloween. The company has determined that their profits per bushel of corn is given by the quation:
P(X) = 20.00 - 5X, where X is the price of corn per bushel six months from today.
To hedge against the prospect of higher corn prices, the company purchases 5 call options on corn with a strike price of $3.75 and a cost of $0.14703 (all dollar calues are per bushel).
The annual continuously compunded risk-free rate is 4%.
a) Calculate the company's after hedge profits per bushel of corn if the actual price of corn in six months is $3.50 per bushel.
b) Calculate the company's after hedge profits per bushel of corn if the actual price of corn in six months is $4.00 per bushel.