6. Nurse Christine Chapel has started a side business in which she makes jewelry from dilithium crystal. After adding in production costs, she figures that her profit (at the end of a one-year period) can be summarized by the equation: 100,000 70ST, where ST represents the spot price of one ounce of dilithium crystal at the end of the year.To hedge her position, Nurse Chapel buys (long) 70 call options on dilithium crystal today with a strike price of 1,300 and one year to expiration. The price of each option is 95.00.The current price of dilithium crystal is 1,200.00 per ounce and the risk-free rate is 5.1293%.

a. Calculate Nurse Chapels after-hedge profits at the end of one year if:

i.The spot price of dilithium crystal at that time is 1,200.00 per ounce (5 points)

ii.The spot price of dilithium crystal at that time is 2,000.00 per ounce (5 points).

b. What must the price of dilithium crystal per ounce be one year from today if Nurse Chapels after-hedge profit is 6,620? (5 points)

c. If instead of using options to hedge, Nurse Chapel used 70 long forward contracts, what after hedge profit could she guarantee? (Assume the forward price is the arbitrage-free price). (5 points)