# Ex1pracq - EXAM PRACTICE QUESTIONS AND SOLUTIONS FIN 4504...

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EXAM PRACTICE QUESTIONS AND SOLUTIONS FIN 4504 Equity and Capital Markets Fall 2004 Instructor: Cem Demiroglu Cem purchases 100 shares of IBM stock at \$100 a share by putting up the minimum amount cash and borrowing the remaining from his broker. The initial margin is 50% and the maintenance margin is 30%. Assume that the interest rate on the broker’s loan is 1% per month. a) How much would to the stock price have to fall (in percentage) at the end of first month before Cem will get a margin call? Initial equity = 50% * 100 * \$100 = \$5,000 Amount borrowed = Value of stock – Initial equity = \$10,000 - \$5,000 = \$5,000 At the end of the month accumulated loan interest is \$5,000 * 1% = \$50 Let’s call the price where margin call comes as P. Then at price = P, [100*P – Loan – Interest Charge] / 100*P = 0.30 [100*P - \$5,000 - \$50] / 100*P = 0.30 P = \$72.14. How much a fall is this? 27.86%! b) Suppose that the price of IBM shares suddenly fell to \$65 at the end of the month. How much money would Cem have to add to his account to maintain ownership of all his IBM stock if the share price falls by the amount in part (a). (Assume that he needs to bring his margin to back to maintenance margin) Total value of the IBM stocks = 100 * \$65 = \$6,500 Minimum acceptable equity position = \$6,500 * (0.30) = \$1,950 Existing equity position = \$6,500 - \$5,000 - \$50 = \$1,450 Required new cash inflow = \$1,950 - \$1,450 = \$500 c) Let’s suppose that the share price falls by the amount in part (b) and Cem does not have any money to add to his account. Therefore, he instructs his broker to sell some of his IBM shares and use the proceeds to pay off a portion of the loan. How many shares does Cem have to sell to comply with the maintenance margin? Number of shares sold = X 1

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Total value of IBM shares after the sale= \$65 * (100 – X) Total loan and interest after partial payment with stock sale proceeds= \$5,050 - \$65 X Total equity position = \$65 * (100 – X) – [\$5,050 - 65 X] = \$1,450 We try to satisfy the following equality: \$1,450 / [\$65 (100 – X)] = 0.3 → X = 25.64 shares d) Suppose that on the first day after Cem’s purchase the stock price increases 20%. Cem considers this as a bullish sign for IBM stock and decides to purchase more stock, though he does not own any more cash to put into his account. He decides to borrow from his broker. How many additional shares of IBM stock can Cem buy at the end of the first day without adding cash to his account? Assume that the interest charge on one day loan is zero. (hint: when shares are added, the account must have enough equity to meet the initial margin requirements.) Equity in account = \$10,000*1.2 - \$5,000 = \$7,000 Initial margin = 50% Maximum loan amount at this margin when equity in account is \$7,000: \$7,000 Existing loans = \$5,000 Possible new loans= \$7,000 - \$5,000 = \$2,000 New price of IBM = \$100 * (1.2) = \$120 Number of new shares purchased on new loan = \$2,000 / \$120 = 16.66 shares 2
Microgen had the following returns over the last four years. Year

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Ex1pracq - EXAM PRACTICE QUESTIONS AND SOLUTIONS FIN 4504...

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