Stock Futures with Dividends

Today is January 3. Your friend David has just bought a futures contract on a stock index, and the contract specifies one year to expiration. The current share price is $80, and the annually compounded interest rate is 10%. The stock will pay quarterly dividends of $2 during the next year, with dividends payments on the following dates:

January 25

April 25

July 25

October 25

Assume that this is a non-leap year.

a.What is the futures price on this contract on January 3?

b. What is the cost-of-carry on this futures contract on January 3?

c. What is the value of this futures contract on February 17 if the spot price turns out to be $90 on that day?

d. Suppose that, instead of paying a quarterly dividend of $2, the stock index has an annual dividend yield of 10%. The continuously compounded interest rate is 10.52%. What is the price of the index futures on January 3? What is its value on February 17 when the index turns out to be $90?