Canada's primary aluminium industry is the fifth largest in the world with an annual production of 2.9 million tons of primary aluminium with the lowest carbon footprint. Alcoa, Aluminerie Alouette and Rio Tinto operate 9 plants in Canada (8 plants in Quebec and 1 in British Columbia). The industry supports more than 8,800 jobs in Canada generating CDN$8.3 billion in exports.

It is February 1st. An aluminium plant in Quebec agrees to deliver 250 metric tons (MT) of aluminium in 9 months to a car part manufacturer in Guelph. The current spot aluminium price is $1,994 per MT, and the risk- free rate of interest is 5% per year with continuous compounding. The aluminium plant has just taken a short position in a 9-month forward contract on 250 metric tons (MT) of aluminium.

a. Suppose that there are no storage costs for aluminium. Calculate the 9-month aluminium forward price for the contract. 

Calculate the value of the forward contract on Febuary1st, 2021, at the time the contract is first entered.

b. Three months later, on May 1st, 2021, the spot price of aluminium is $1990 per MT, and the risk-free rate of interest is still 5% per year.

 Calculate the forward price and the value of the short forward position on May 1st, 2021?

c. In Question 1.a, suppose now there are storage costs. The storage costs are $144 per MT per year payable quarterly in advance. The risk-free rate of interest is still 5% per year. On February 1st, 2021, calculate the present value of the storage costs for the 9 months. 

Calculate the forward price of aluminium on February 1st, 2021.

d. In Question 1.a, suppose now there is a storage rate of 4.0% per year and the aluminium plant obtains a convenience yield of 1.0% per annum from holding inventory of aluminium. The risk-free rate of interest is still 5% per year. On May 1st, 2021 (three months later), the spot price of aluminium is $1990 per MT.

 Calculate the forward price of the contract on May 1st, 2021. Calculate the value of the long forward contract on May 1st, 2021.