Power Associates is a one-year firm that wants to perfectly hedge its cash flows next year. That is, it wants to completely eliminate the riskiness of its cash flows by selling a certain number of futures contracts on a commodity index. The table below details the cash flows produced by Power Associates and the value of the commodity index in each possible state of the world next year:
Assume that the expected return on Power Associates and the commodity index are 20 percent. Also assume a risk-free rate of 5 percent.
a) What is the value of Power Associates?
b) What is the one-year futures price on the commodity index?
c) How many index futures contracts would you have to sell to perfectly hedge the Power cash flows?
d) What is the expected cash flow next year from the futures position? This number should be negative - explain why this is the case.
e) What is the value of Power Associates now that it has hedged its cash flows? Compare this value to the value you calculated in part (a).