Suppose that you want to manage a chain of coffee shops across the US. You are worrying about coffee price increases and would like to lock-in the price at which you can buy coffee each second month over the next year. Your total demand over the year is 36 million pounds, with equal amounts needed at the end of each two months. Suppose that the risk-free rate of interest is 5% with continuous compounding. In order to lock-in your price over the next year, you consider buying exchange-traded futures contracts. You check the internet to get price quotes for coffee futures contracts traded on the Chicago Mercantile Exchange(CME), and you get the following price structure.

CME coffee futures prices Contract size: 37,500 pounds Months to Maturity Dollars per pounds 1.9330 1.9750 1.9980 2.0145 2.0215 2.0265 4 6 10 12 (a) (15 points) Suppose that you want to hedge your exposure using CME futures How many of each contract should you buy initially when you can take telescoping futures position? (Each futures contract is for 37,500 lbs.) (b) (20 points) Suppose that you decide to try and negotiate a "fixed-price, fixed- supply" contract with a commodity swap dealer. Under the terms of the swap, you would pay a "fixed-price" per pound in each two months of the contract, and receive a "fixed supply" of 6 million pounds at the end of each two months Assuming that you are indifferent between buying futures and buying the fixed- price, fixed-supply contract from a delivery standpoint, what is the maximum price per 37,500 pounds that you are willing to pay