Canadian Petroleum has reserves of 200,000 barrels of oil that can be extracted at the end of the year. The current spot price of crude oil is $70 per barrel and CPs cost of extraction is $40 per barrel. The risk-free rate is 5% per year (CCR), the net convenience yield for oil is assumed to be 2% per year (CCR), and the volatility for oil is 40% per year. CP has fixed costs of $4 million next year. (Assume all revenues and costs occur at the end of each year.)

a. What is the one-year forward price of crude oil?

b. What is CPs hedged profit per barrel next year if it sells forward at the forward price?

c. How many forward contracts are needed to hedge its fixed costs?

d. If CP hedges its fixed costs using forward contracts, how much free cash would it have next year if the oil price turns out to be $100?

e. Use the Black-Scholes framework to determine the price of a European call option on crude oil with strike price $75 and one year until expiration.

f. What is the value of a European put option on crude oil with strike price $75 and one year until expiration?

g. What is CPs hedged profit per barrel next year if it hedges using put options, and the oil price turns out to be less than $75/bbl?

h. How many put options are needed to hedge its fixed costs?

i. If CP hedged its fixed costs using put options, how much free cash would it have next year if the oil price turns out to be $100?