Problem 16 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. 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. Problem 17You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share.. a. How much in cash or securities must you put into your brokerage account if the brokerâs 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? Problem 23 Suppose that Intel currently is selling at $40 per share. You buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%. a. What is the percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to: (i) $44; (ii) $40; (iii) $36? What is the relationship between your percentage return and the percentage change in the price of Intel? b. If the maintenance margin is 25%, how low can Intelâs price fall before you get a margin call? c. How would your answer to ( b ) change if you had financed the initial purchase with only $10,000 of your own money? d. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if Intel is selling after one year at: (i) $44; (ii) $40; (iii) $36? What is the relationship between your percentage return and the percentage change in the price of Intel? Assume that Intel pays no dividends.e. Continue to assume that a year has passed. How low can Intelâs price fall before you get a margin call? Problem 24Suppose 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 Intelâs price rise before you get a margin call?c. Redo parts ( a ) and ( b ), but now assume that Intel also has paid a year-end dividend of $1 per share. The prices in part ( a ) should be interpreted as ex-dividend, that is, prices after the dividend has been paid.
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