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.

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

1) Total investment= 1000*40=40,000

With 50% margin $ 20,000 will be equity and $ 20,000 will be borrowed.

Interest on the borrowed amount: 20,000*0.04= 800

Therefore, stock price fall for margin call:

Borrowed + Interest Cost/(1-Maintanence Margin)

=$ 20,000+ 800/(1-0.30)

=$ 29,714.29

Therefore, price per share: 29,714.29/1000=29.714

If the investor had done a cash account transaction then the return would be:

29.714/40-1= -25.715%

2) Value of the stocks at price of $ 45= 1000*45= $ 45,000

Therefore, your margin buying power is = 45,000/0.50= $ 22,500

3) Investor only needs to maintain the maintenance margin. The rest he can withdraw. Maintenance margin:

=(0.30*45,000)= $ 13,500

The amount that can be withdrawn is: $ 22,500-13,500 =$ 9,000

4) Value of the shares shorted = 1000*40=$ 40,000

Deposit= 30,000

Borrowed= $ 10,000

Therefore, interest cost= 10,000*0.04=$ 400

Therefore, stock price rise for margin call:

10,000 -400/(1-0.30)= $ 13,714.29

Therefore, price per share before you get margin call:

(40,000+13,714.29)/1000= 53.714