PROBLEMS1. You have $40,000 to invest in Sophie Shoes, a stock selling for $80 a share. The initial
margin requirement is 60 percent. Ignoring interest and commissions, show in detail the
impact on your rate of return if the stock rises to $100 a share and if it declines to $40 a
share, assuming (a) you pay cash for the stock, and (b) you buy the stock using maximum
leverage.
2. Lauren has a margin account and deposits $50,000 into it. Assume the prevailing margin
requirement is 40 percent, interest and commissions are ignored, and the Gentry Wine
Corporation is selling at $35 per share.
a. How many shares can Lauren purchase using the maximum allowable margin?
b. What is Lauren’s profit (loss) if the price of Gentry’s stock
i. rises to $45 and Lauren sells the stock?
ii. falls to $25 and Lauren sells the stock?
c. If the maintenance margin is 30 percent, to what price can Gentry Wine fall before
Lauren will receive a margin call?
3. Assume that you buy 100 shares of Francesca Industries stock on 55 percent margin when
the stock is selling at $20 a share. The broker charges a 5 percent annual interest rate, and
commissions are 2 percent of the stock value on the purchase and sale. A year later you
receive a $0.50 per share dividend and sell the stock for $27 a share. What is your rate of
return on Francesca Industries?
4. You decide to sell short 100 shares of Charlotte Horse Farms when it is selling at its yearly
high of $56. Your broker tells you that your margin requirement is 45 percent and that the
commission on the purchase is $155. While you are short the stock, Charlotte pays a $2.50
per share dividend. At the end of one year, you buy 100 shares of Charlotte at $45 to close
out your position and are charged a commission of $145 and 8 percent interest on the
money borrowed. What is your rate of return on the investment?92 Part 1: The Investment Background5. You own 200 shares of Shamrock Enterprises that you bought at $25 a share. The stock is
now selling for $45 a share.
a. You put in a stop loss order at $40. Discuss your reasoning for this action.
b. If the stock eventually declines in price to $30 a share, what would be your rate of
return with and without the stop loss order (ignore commissions)?
6. Two years ago, you bought 300 shares of Kayleigh Milk Co. for $30 a share with a marginof 60 percent. Currently, the Kayleigh stock is selling for $45 a share. Assuming no divi-
dends and ignoring commissions, compute (a) the annualized rate of return on this invest-
ment if you had paid cash, and (b) your annualized rate of return with the marginpurchase.
7. The stock of the Madison Travel Co. is selling for $28 a share. You put in a limit buy
order at $24 for one month. During the month the stock price declines to $20, then
jumps to $36. Ignoring commissions, what would have been your rate of return on this
investment? What would be your rate of return if you had put in a market order? What
if your limit buy order was at $18?