2. An investor opens a margin account with a discount broker. The initial margin

Question

2. An investor opens a margin account with a discount broker. The initial margin requirement is 50%. The maintenance margin is 30%. The investor intends to buy 1000 shares of XYZ at $40. An interest rate on the margin loan is 4% per year. The stock does not pay any dividends. (30 points

a) How much money must the investor deposit?

b) Assuming the investor deposits $30,000 (NOT the amount you calculated in part (a) and buys the shares. How far could the stock price fall before the investor would get a margin call?

c) Assuming the stock price reaches the price you calculated in part (b) and the investor receives a margin call. How much money must the investor deposit to avoid the liquidation actions by the broker? d) Assume that the investor receives a margin call in one year after purchasing the stock, but instead of depositing the amount calculated in part (c) he or she sells the shares. What is the rate of return realized by the investor?

e) Assume the investor has a cash account (not margin account) and he or she sells the shares at the price you calculated in part (b). Recalculate the investor’s rate of return. f) Assume in one year the stock’s price did not fall but increased to $45, and the investor holds the shares. What is the buying power of his or her margin account? g) Assuming the situation described in part (f), how much can the investor withdraw in cash? h) Assuming the investor decides to short sale the stock (instead of buying it in the beginning) and receives $40 per share. If he/she deposits $30,000 (as stated in part (b), how far can the stock price raise before the investor receives a margin call?

Explanation / Answer

a) Investor should deposit Initial Margin only which is 50% Initial Margin Money = (1000 shares * $40 ) * 50%                                        =$20000 b) Equity = Value of securities - Borrowing(Margin Provided by broker)             =$40000 - ($40000 - $30000)             =$30000 Margin = (No. Of Shares * Price per share) - Borrowing / No. Of shares * Price per share            30% = (1000*P - 10000) / 1000*P         300P = 1000P - 10000      P = 14.28 (Approx) c) Money to be deposited at margin call = Initial Margin Required - Value of security                                                                     =20000 - 14.28*1000                                                                     = 5720 d) Rate of Return =[( Closing Value of equity - Initial Value of equity) - Margin Loan Payoff - Interest Payment on margin] / Initial Investment                            =[(14280-30000)-10000 - 400] / 30000                            = -26120/30000                            = - 87.07% e) Rate of Return = (Closing Value of Equity - Initial Value of Equity ) / Initial Investment                             =(14280 - 40000) / 40000                            =64.3% f) Buying Power = Total Buying power - buying power used Total Buying power = (10000 * 45 ) * (100%-30%)                                      =45000*70%                                      =31500 Buying Power Used = 20000 Buying Power Left = 31500-20000 = 10000 g) Maximum amount which can be withdraw by investor = Equity - Borrowing                                                                                                    =25000 - 20000                                                                                                    =5000 h) Margin = (Amount received from Short sell + Margin Borrowing - Value of Investment)/Value of Investment            30% = (40000 + 30000 - (1000*P))/1000*P         300P = 70000 - 1000P         700P = 70000              P = 100

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