Question

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.

How much money must the investor deposit?

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?

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?

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?

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.

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?

Assuming the situation described in part (f), how much can the investor withdraw in cash?

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?

Answer 1

Scenario-1

Investor buys 1000 shares @$40

Total=40*1000=$40,000

Margin account need 50% therefore, the investor need to deposit 50% into the margin account

=40,000(0.5)=$20,000 into the account.

Scenario 2

An investor invests $30,000

Total stock worth in the account=$60,000 (50% deposited+50% margin)

He will get a margin call at 30%

The stock he bought=60,000/$40=1500 shares

Margin call comes at 30,000(0.3)=$9,000

Total margin account=30,000(on margin)+$9000(Initial investment by investor reduced)

At $39,000 of the account or 39000/1500 shares

or when share hit at 39000/1500=$26/share, the investor will get a margin call.

The money he needs to deposit is 39,000(0.5)=18,500 is the requirement out of which 9000 was deposited

Therefore he needs to deposit 18500-9000=$9500 into his account.

Return realized by investor:

Loan on margin=4%

interest=30,000(0.04)=$1200

new price of stock=26$(as caluclated above)

Net in=(26*1500)-30,000-1200-30,000(margin)

=39,000-30,000-1200-30,000

=(-)22,200(loss) or 73.33 % loss

Cash account

amount invested =$30,000

Buys 750 share @$40/share

New pirce=$26*750=$19500

Rate of return=($19500/30,000)-1

Loss = 35%

Scenario 4

New stock price=$45

Value of postion=$45*1500=67500

Selling

Profit=67500-30,000-1200(interest on margin)-30,000

=$6300

Rate of return=(36300/30,000)-1

=21% profit on investment