(Commodity Forward Pricing) Consider the following oil forward contract: - Notional amount: 1 bbl; - Delivery Date: One year from now; - Interest rate: 0.06 per annum continuously compounded; - Convenience yield: zero (for simplicity); - Storage cost rate: 0.04 per annum continuously compounded (in other words, X bbd of oil at time 0 will decay to Xexp(0.04T) bbl at time T); - The current spot price: $50/bb1. Theoretically speaking, the forward price should be 50e+1(0.06+0.04)=$55.2585/bbl. However, your counterparty quoted a forward price of $60/bbl. Because this forward contract with forward price of $60/bbl is overpriced, you should do the following arbitrage strategy: At time 0 : - Take a short position of the overpriced forward contract (forward price =$60/bbl); - Borrow 50e+1(+0.04) dollars, and buy e+1(+0.04) bbl of oil from the spot market (spot price =$50/bbl). Between time 0 and 1 : - Store e+1(+0.04) bbl of oil to your storage. At time 1 , your oil will reduce to 1bbl. (Assume that you have sufficient amount of vacant oil storage.) At time 1: - Deliver 1bbl of oil to your counterparty of the forward contract. - Repay X dollars to the person who lent the money at time 0 . - Receive $60/bbl (=forward price) With these being said, please, answer the following question. a) What is the cash flow at time 0 ? b) What should be X dollars you need to repay to the person who lent the money at time 0 ? c) What is the arbitrage profit at time 1