Question #7: Margin [20 Points] Gwendolyn opens up a trading account at Charles
ID: 1093397 • Letter: Q
Question
Question #7: Margin [20 Points]
Gwendolyn opens up a trading account at Charles Schwab and purchases 800 shares of Logitech Stock
(LOGI) at $15 per share. Suppose that the initial margin percentage is 66.67% and that your broker
charges you a margin interest rate of 4%.
(a) What is the minimum amount that Gwendolyn must deposit into her account in order to buy 800
shares of Logitech on margin? [6 Points]
(b) Suppose that Gwendolyn deposited the amount in Part (a) and borrowed the balance to purchased the
800 shares of Logitech. What will be her rate of return if the price of Logitech stock goes up by 10%
during the next year? You may ignore any expected dividend payments. [Make sure to take into account
the margin interest rate in your calculations.] [8 Points]
(c) How far would the price of Logitech have to fall before Gwendolyn receives a margin call if the
maintenance margin is 30%? [6 Points]
Explanation / Answer
Amount required to purchase 800 logitech shares = 800*15 = $12,000
Initial margin = 66.67% * 12000 = $8000.4
Borrowed amount on which margin interest rate will apply = 12000 - 8000.4 = 3,999.60
a. Gwendolyn must deposit $8000.4 in her account as initial margin to buy 800 logitech shares
b. Share price 1 year later = 15 + 15*10% = $16.5
Total return from share sale = 800 * (16.5-15) = 800*1.5 = 1200
Interest paid on margin = 4% * 3999.60 = $159.984
Total return = 1200 - 159.984 = 1040.016
capital Invested by Gwendolyn = initial margin = $8000.4
Rate of return = 1040.016/8000.4 * 100 = 12.999% or 13.00%
c. Let the stock price be P
Total Amount = 800P
maintenance margin will be triggered when (Current market value - amount borrowed)/Current Market VAlue = 30%
(800P - 3999.6)/800P = 0.30
800P - 3999.6 = 0.3*800P = 240P
800P - 240P = 3999.6
560P = 3999.6
P = 3999.6/560 = $7.14
Thus, maintenance margin will be triggered if share price falls below $7.14