• This margin requirement (the proportion of total
transaction value that must be paid in cash)
– If it is 40 percent (allowing loans of 60 percent of the value)
– 100 percent (allowing no borrowing).
– Lower margin requirements allow you to borrow more
• The
leverage factor = 1/percent margin
.
• If margin req. = 0.6, find leverage factor
– leverage factor = 1/0.6=1.67 – Thus, the
– rate of return on the stock= rate of return x leverage factor
Problem 1
• The initial margin requirement is 60 percent
(allowing loan 40%).
• You have $40,000 to invest in a stock selling
for $80 a share.
• Ignoring taxes and commissions and interest.
• 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, (100% margin requirement) and
(a) you pay cash for the stock Number of shares you could purchase = $40,000/$80 = 500 shares.
The leverage factor for a 60 percent margin requirement is = 1/percentage margin requirement = 1/.60 = 5/3
Thus, the rate of return on the stock if it is later sold at $100 a share = 25.00% x 5/3 = 41.67%.
The rate of return on the stock if it is sold for $40 a share: = -50.00% x 5/3 = -83.33%.
Problem 2
• Lauren has a margin account and deposits $50,000.
Assuming the prevailing margin requirement is 40 percent (can borrow 60%), commissions are ignored, and The
Gentry Shoe Corporation is selling at $35 per share:
a. How many shares of Gentry Shoe can Lauren purchase using the maximum allowable margin?
b. What is Lauren’s profit (loss) if the price of Gentry’s stock
– (1) Rises to $45? – (2) Falls to $25?
c. If the maintenance margin is 30 percent, to what price can Gentry Shoe fall before Lauren will receive a margin call?
• $50,000 deposit must represent 40% of her total investment.
• Thus, $50,000 = .4x then x = $125,000.
• Since the shares are priced at $35 each, Lauren can purchase $125,000 / $35 = 3,571 shares (rounded).
(1) If stock rises to $45/share, Lauren’s total return is: • 3,571 shares x $45 = $160,695.
• Total profit = $160,695 - $125,000 = $35,695 (2) If stock falls to $25/share, Lauren’s total return is: • 3,571 shares x $25 = $89,275.
Check
• NS
MPS total Worth
• 3571
30 107130
•
• loan
eq maint. Margin
Problem 3
• Suppose you buy a round lot of Maginn Industries stock on 55 percent margin when the stock is selling at $20 a share. (Round lot holders are holders of 100 shares or more)
• The broker charges a 10 percent annual interest rate, and • commissions are 3 percent of the total stock value on
both the purchase and sale.
• A year later, you receive a $0.50 per share dividend and sell the stock for 27.
• The rate of return on investment = profit / initial investment
• Where profit = Ending Value - Beginning Value + Dividends - Transaction Costs (sale & purchase) – Interest
• Initial Investment=Margin req. + commission (purchase)
• Suppose Round lot = 100 shares
• Beginning Value of Investment = $20 x 100 shares = $2,000
• Investment = margin requirement + commission.
• = (.55 x $2,000) + (.03 x $2,000)
• = $1,100 + $60
• The Ending Value of Investment = $27 x 100 shares = $2,700
• Dividends = $.50 x 100 shares = $50.00
• Transaction Costs (Commission)= (.03 x $2,000) + (.03 x $2,700) = $60 + $81
• = $141
• Debt amount = 0.45*$2000
• Interest = .10 x (.45 x $2,000) = $90.00
• Profit = Ending Value Beginning Value + Dividends -Transaction Costs – Interest
• Profit = $2,700 - $2,000 + $50 - $141 - $90 = $519 • The rate of return on your investment of $1,160 is:
Problem 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.
• Profit on a Short Sale = Beginning Value Ending Value -Dividends -Trans. Costs - Interest
• Beginning Value of Investment = $56.00 x 100 shares = $5,600 (sold under a short sale arrangement)
• Your investment = margin requirement + commission = (.45 x $5,600) + $155
= $2,520 + $155 = $2,675
• Dividends = $2.50 x 100 shares = $250
• Ending Value of Investment = $45.00 x 100 = $4,500
(Cost of closing out position)
• Transaction Costs = $155 + $145 = $300
• Interest = .08 x (.55 x $5,600) =$246.4
• Profit = $5,600 - $4,500 - $250 - $300 - $246.40 = $303.6 • The rate of return on investment $303.60/$2,675 = 11.35%
Problem 5
• You own 200 shares of Shamrock Enterprises that you bought at $25 a share.
• The stock is now selling for $45 a share.
• a. If 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?
