FINANCE 261 Question 6 (10 marks) Cobalt (a rare carth metal) is an essential so
ID: 2617241 • Letter: F
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FINANCE 261 Question 6 (10 marks) Cobalt (a rare carth metal) is an essential source material used in the manufacture of the current generation of rechargeable batteries. ALSET Corporation is planning to construct a "tera- factory" even bigger than a giga-factory- to produce rechargeable batteries. However it is concerned about the future cost of cobalt, and would like to "lock-in" the price of 15,000kg of cobalt for use in 1 years' time (when its tera-factory is expected to be ready to start production). ALSET Corporation can borrow at the risk free rate, with interest payable annually in arreans The following information is available: Risk free rate: Market risk premium: ALSET Corporation beta: Spot (current) price for lkg of physical cobalt: Storage cost of cobalt: 4% per annum. 5% per annum 1.3 $83 /kg S2 per kg. per year (payable up-front) Futures price for lkg of physical cobalt (1 year): 92/kg a) Calculate the total dollar amount ALSET Corporation would need to pay in 1 years' time if it secured all its future cobalt needs by buying futures. (1 mark) b) The CFO suggests an alternative strategy to "lock-in" the cost of cobalt: ALSET Corporation should pay cash to buy all the cobalt it needs at the spot price and in addition pay up-front for 1 years' worth of storage. The total cost this entails can be borrowed, to be repaid (with interest) in 1 years' time. What is the total dollar amount ALSET Corporation would need to pay to clear its borrowing at the end of one year? (4 marks) Which of a) or b) would be preferred by ALSET Corporation on a pure cost basis? How much money would ALSET Corporation save by taking the lowest cost option c) (2 mark) Let the annual risk-free rate be r, the spot price of Ikg of cobalt be S and the up-front storage cost of lkg for T years be C. Derive the no-arbitrage futures price fof lkg of cobalt in terms of r, S and C and T. Hint: you already calculated the I year no-arbitrage futures price for 15,000kg in (b). d) (3 marks) (Total for question: 10 marks)Explanation / Answer
Answer a) Cost to be paid in 1 year time = quantity * future price = 15000 * 92 = $ 13,80,000
Answer b) Total cost = Cost @ spot market + interest charged + storage cost
= 15000 * 83 + 15000*83*4% + 2*15000 = $ 13,24,800
Answer C) As cost of option A < the cost of option B ,
So, option in B is better than option in a
Answer D)
no arbitrage formula for future cost
F = S +S*r + S*C*T = S (1 +r +CT).
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