The SPACE share price is $40 now and its dividend is $2 per share in the year. The Dealer in the market is ready to lend shares to investors for short sale, and lend money to investors for purchase by margin. The interest rate is 5% per year for money loan only and zero for share loan. The initial margin ratio is 40% for either short sale or purchase by margin.

Please explain with calculations.

Required:

a. Suppose that Christina is bearish on the SPACE share and she short sells 3,000 shares at the beginning of the year. Suppose also the share price is $30 at the end of the year. (1) What is the remaining margin ratio in Christinas account? (2) What is the rate of return of Christinas investment?

b. Suppose that David is bullish on the SPACE share and he buys 3,000 shares by margin at the beginning of the year. Suppose also the share price is $30 at the end of the year. (1) What is the remaining margin ratio in Davids account? (2) What is the rate of return of Davids investment? (3) If the maintenance margin is 15%, at what market price David will receive a margin call? Assume the price fall happens immediately (the interest and dividend are not accrued).

c. At the beginning of the year after the initial trading, what are the total asset and equity (margin) respectively in Christinas account? What are the total asset and equity (margin) respectively in Davids account?

d. Briefly discuss the investors incentives/motivations when they trade securities by short sale and purchase on margin respectively.