Problem 4. Firm BestHockeySticks needs to buy rubber to manufacture their hockey

Question

Problem 4. Firm BestHockeySticks needs to buy rubber to manufacture their hockey pucks. Specifically, they need to buy 3 tons of rubber for next winter, January 2017 (T = 3/4). The future price of rubber is uncertain. Each ton of rubber can be used to manufacture 1000 pucks, each of which is sold for $2.50. The manufacturing has a fixed cost of $1200 per ton, plus the cost of rubber. Suppose that today rubber sells for $900/ton and interest rates are r = 10% continuously compounded, annual.

• BestHockeySticks buys 2 Call options with strike K = 900 (the option allows to buy rubber for $1000/ton) at an upfront cost of $100 each. Write down a mathematical formula for the resulting net profit of BestHockeySticks at T = 1. Sketch the profit as function of future rubber price.

• In addition to the above Call options, BestHockeySticks decides to enter into a Forward contract to purchase 1 ton of rubber at a fixed price of $970/ton. Plot the resulting net profit diagram of BestHockeySticks (rubber + forward + Calls). Label important points on the graph.

Explanation / Answer

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