2. Suppose I short 100 shares of stock XYZ which currently is priced at $100. I agree to return the stock shares in exactly 1 year. Suppose the stock borrowing rate is $1 per share per year. During the course of the year I know the stock will pay dividends of $2 per share at the end of the year and I also know that the price of the stock will fall to $90 per share. Suppose the current discount rate for such an investment is 5% annually.

a) What is the present value of my short selling investment?

b) Now suppose that the stock price will either fall to $90 (with probability 75%) or go up to $105 (with probability 25%).

What is the expected present value of my short selling strategy?