5 Ch04 Problems

• 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 – (b) you buy it using maximum leverage.

(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) • • (2) • •

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 If stock falls to $25/share, Lauren’s total return is: 3,571 shares x $25 = $89,275. Total loss = $89,275 - $125,000 = -$35,725.

Check • • • • •

NS 3571

MPS total Worth 30 107130

loan 75000

eq maint. Margin 32130 0.29991599

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. • What is your rate of return on the investment?

• 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 • = $1,160

• 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: $519/$1,160 = 44.74%

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. • What is your rate of return on the investment?

• 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?