The risk-free interest rate is fixed at5% per annum with continuous compounding for all maturities. ABC is a public firm that is expected to pay no dividend. Round to the nearast thousandth (the third digit after decimal point).

(1.1) On Feb 1st, the spot price of ABC is $52. Suppose Bill entered into a short position of 1 million shares of ABC on Feb 1st using a one-year forward contract. Suppose that the forward price is set to satisfy the no-arbitrage condition. What is the one-year forward price of ABC? What is the notional value of Bills position. What is the value of Bills position in the forward contract?

(1.2) On Sep 1st, spot price of ABC becomes $53. What is the 5-month forward price of ABC on this day? What is the value of Bills forward position now? What is the notional value of his position?

(1.3) Is it possible for Bill to earn profits when spot price of ABC increases? Find the spot price on Sep 1st that would make Bill earn zero profit from his forward position.

(1.4) On Oct 1st, ABC unexpectedly announces that it will issue a one-time dividend of $3 on Dec 1st. Market reacts negatively to the announcement and the spot price of ABC falls immediately from $54 to $53 per share. What is the value of Bills forward contract right after the announcement? Can Bill eliminate the risk in his profit of his forward contract position by entering into a new forward position? If so, describe all his trades on Oct 1st and Feb 1st.

(1.5) More generally, we have two formula so 0f forward prices: (1)F(0,T)=S(0)e(r+g)T and(2)F(0,T)= (S(0)+PV (E0,T )) erT , where g is the continuously compounded cost of carrying the asset and PV (E0,T ) equals the present value of the cost of carrying the asset. Find the equivalent g for a given PV (E0,T ). Find the equivalent PV (E0,T ) for a given g.