FINC 351 Practice Problems 3

12. Suppose you short-sell 100 shares of IBM, now selling at $200 per share. (LO 3-4) a. What is your maximum possible loss?

12 a. 12 In principle, potential losses are unbounded, growing directly with increases in the price of IBM.

15. Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. (LO 3-4) a. What is the margin in Dée's account when she first purchases the stock? b. If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call? c. What is the rate of return on her investment?

15. a The stock is purchased for $40 x 300 shares = $12,000. Given that the amount borrowed from the broker is $4,000, Dee's margin is the initial purchase price net borrowing: $12,000 - $4,000 = $8,000. b If the share price falls to $30, then the value of the stock falls to $9,000. By the end of the year, the amount of the loan owed to the broker grows to: Principal x (1 + Interest rate) = $4,000 x (1 + 0.08) = $4,320. The value of the stock falls to: $30 x 300 shares = $9,000. The remaining margin in the investor's account is: Margin on long position = "Equity in account " /"Value of stock" = "$9,000 － $4,320" /"$9,000" = 0.52 = 52% Therefore, the investor will not receive a margin call. c Rate of return = "Ending equity in account － Initial equity in account" /"Initial equity in account" = "$4,680 － $8,000" /"$8,000" = - 0.4150 = - 41.50%

On Jan 1, you sold short one round lot (100 shares) of Zenith stock at $14 per share. On March 1, a dividend of $2 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $9 per share. You paid 50 cents per share in commissions for each transaction. What is the value of your account on April 1?

17. The proceeds from the short sale (net of commission) were: ($14 x 100) - $50 = $1,350 A dividend payment of $200 was withdrawn from the account. Covering the short sale at $9 per share cost you (including commission): $900 + $50 = $950 Therefore, the value of your account is equal to the net profit on the transaction: $1350 - $200 - $950 = $200 Note that your profit ($200) equals (100 shares x profit per share of $2). Your net proceeds per share was: $14 selling price of stock -$9 repurchase price of stock -$2 dividend per share -$1 2 trades x $0.50 commission ea. $2

18. You are bullish on Telecom stock. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. (LO 3-4) a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? (Ignore the expected dividend.) b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.

18. Price per share $50 Equity invested $5,000 Borrowed funds $5,000 Interest rate 8.00% Total investment $10,000 Price change 10.00% Margin required 30.00% Your initial investment is the sum of $5,000 in equity and $5,000 from borrowing, which enables you to buy 200 shares of Telecom stock: "Initial investment" /"Stock price" = "$10,000" /"$50" = 200 shares The shares increase in value by 10%: $10,000 * 0.10 = $1,000. You pay interest of = $5,000 * 0.08 = $400. The rate of return will be: "$1,000 － $400" /"$5,000" = 0.12 = 12% The value of the 200 shares is 200P. Equity is (200P - $5,000), and the required margin is 30%. Solving "200P －$5,000" /"200P" = 0.30, we get P = $35.71. You will receive a margin call when the stock price falls below $35.71.

19. You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share. (LO 3-4) a. How much in cash or securities must you put into your brokerage account if the broker's initial margin requirement is 50% of the value of the short position? b. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?

19. Initial margin is 50% of $5,000, which is $2,500. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin). Liabilities are 100P. Therefore, net worth is ($7,500 - 100P). Solving " $7,500－100P" /"100P" = 0.30, we get P = $57.69. A margin call will be issued when the stock price reaches $57.69 or higher.

9. How do margin trades magnify both the upside potential and downside risk of an investment portfolio?

9 Margin is a type of leverage that allows investors to post only a portion of the value of the security they purchase. As such, when the price of the security rises or falls, the gain or loss represents a much higher percentage, relative to the actual money invested.

16. Old Economy Traders opened an account to short-sell 500 shares of Internet Dreams at $30 per share. The initial margin requirement was 55%. A year later, the price of Internet Dreams has risen from $30 to $35, and the stock has paid a dividend of $1 per share. What's the remaining margin (in dollar value) in the account? If the maintenance margin is 35%, will Old Economy receive a margin call?

The initial margin was .55×500×$30 = $8,250. The firm loses 30−35 = $5 per share, plus a payment of $1 dividend pay share, or a total loss of $6 per share or $6×500 = $3,000 of loss. Remaining dollar margin: $8,250−$3,000 = $5,250. Margin ratio: 5250 500(35) < 35%. Yes, the firm will receive a margin call.

26. Suppose that you sell short 500 shares of Intel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account. a. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if Intel stock is selling at (i) $44; (ii) $40; (iii) $36? Assume that Intel pays no dividends. b. If the maintenance margin is 25%, how high can Intel's price rise before you get a margin call?

a. If you earn no interest in the funds in your margin account, what will be your rate of return after 1 year if Intel stock is selling at (i) $44 (ii) 40 (iii) 36? Assume that Intel pays no dividends. The gain or loss on the short position is: (-500 X change in price) Invested funds = $15,000 Therefore: rate of return = (-500 x change in price)/15,000 The rate of return in each of the three scenarios is: rate of return = (-500 x $4)/$15,000 = -0.1333 = -13.33% rate of return = (-500 x $0)/$15,000 = 0% rate of return = [-500 x (-$4)]/$15,000 = +0.1333 = +13.33%

You've borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share. a) Will you receive a margin call? b) How low can the price of Disney shares fall before you receive a margin call?

a. You will not receive a margin call. You borrowed $20,000 and with another $20,000 of your own equity you bought 1,000 shares of Disney at $40 per share. At $35 per share, the market value of the stock is $35,000, your equity is $15,000, and the percentage margin is: $15,000/$35,000 = 42.9% Your percentage margin exceeds the required maintenance margin. b. You will receive a margin call when: (1000P - $20,000)/1000P = 0.35 --> when P = $30.77 or lower