Firm BestHockeySticks needs to buy rubber to manufacture their hockey pucks. Spe
ID: 2761963 • Letter: F
Question
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 $900/ton) at an upfront cost of $100 each. Write down a mathematical formula for the resulting net profit of BestHockeySticks at T = 3/4. 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
Price of 1 Hockey Puck = $2.50
Price of 1000 Hockey Puck = $ (2.50 * 1000) = $ 2,500
Quantity of rubber used to manufacture 1000 pucks = 1 ton
Let, Cost of Rubber = $ Y per ton
Fixed Cost in manufacturing = $1200 per ton
Total cost involved in manufacturing 1000 pucks = $ (1200 + Y)
Profit involved in selling 1000 pucks (P) = Price - Total Cost = $ [ 2,500 - (1200 + Y) ] = $ (1,300 - Y)
Strike Price of Call Option (K) = $ 900
Option Premium (C) = $ 100
Future Market Price of Rubber = S
If the firm exercises the call option to buy rubber (S > K), then Y = K + C = $ 1,000
If the firm does not exercise the call option to buy rubber (S < K), then Y = C + S = $ (100 + S)
Profit(P) as function of future rubber price (S):
If S > 900, P = $ (1,300 - 1,000) = $ 300 per 1000 pucks.
If S < 900, P = $ (1,300 - 100 - S) = $ (1,200 - S) per 1000 pucks.
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