# Question: Angie Cowler bought 300 shares of INV stock four years

Angie Cowler bought 300 shares of INV stock four years ago when it was selling for $10 per share. At that time, she really believed that the stock was “a diamond in the rough,” so she borrowed to purchase the maximum amount possible. The initial margin requirement was 55 percent, and the broker loan rate was 10 percent. Today, the stock is selling for $30 per share, and the margin requirements are the same as when Angie first purchased INV. INV reinvests all of its earnings in capital budgeting projects, so it has not paid dividends since its stock began trading publicly.

Even though INV’s stock is now selling for $30, its price has dropped from a historically high price of $38 just a few months ago. Angie doesn’t want to sell the stock because she believes that the stock price will return to its upward trend within the next few months. For this reason, Angie is considering taking the advice of one of her friends, who has suggested that she short sell 100 shares of INV to protect a portion of her gains if the stock price drops further in future months. Her friend has explained that if she decides to sell her stock after more declines, the short sale position will help offset some of the losses she will earn on her long position in the stock.

a. Assume that the price of INV is $20 per share in one year and that Angie does not short sell the stock. What return would she earn on the stock for the year? Remember that Angie is in a margined position.

b. Assume that the price of INV is $20 per share in one year and that Angie short sells 100 shares of the stock at the beginning of the year. What return would she earn on the stock for the year?

c. Compute Angie’s five-year holding period return given the situation presented in part (a).

d. Compute Angie’s five-year holding period return given the situation presented in part (b).

e. Rework parts (a) through (d) assuming that the price of INV is $40 in one year.

Even though INV’s stock is now selling for $30, its price has dropped from a historically high price of $38 just a few months ago. Angie doesn’t want to sell the stock because she believes that the stock price will return to its upward trend within the next few months. For this reason, Angie is considering taking the advice of one of her friends, who has suggested that she short sell 100 shares of INV to protect a portion of her gains if the stock price drops further in future months. Her friend has explained that if she decides to sell her stock after more declines, the short sale position will help offset some of the losses she will earn on her long position in the stock.

a. Assume that the price of INV is $20 per share in one year and that Angie does not short sell the stock. What return would she earn on the stock for the year? Remember that Angie is in a margined position.

b. Assume that the price of INV is $20 per share in one year and that Angie short sells 100 shares of the stock at the beginning of the year. What return would she earn on the stock for the year?

c. Compute Angie’s five-year holding period return given the situation presented in part (a).

d. Compute Angie’s five-year holding period return given the situation presented in part (b).

e. Rework parts (a) through (d) assuming that the price of INV is $40 in one year.

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