Question

(3) An investor buys $8,000 worth of a stock priced at $40 per share using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance margin.

1. In one year the investor has interest payable and gets a margin call. What is the stock price that triggers the margin call?
2. How much additional cash should the investor put in his account to restore the 50% initial margin after receiving the margin call?
3. Suppose that the investor didn’t put in additional cash to satisfy the margin call. As a result, the brokers liquidated his position at the price that triggered the margin call. What is the investor’s return from the investment in this stock?

Answer 1

Answer A

Shares of holding:    8,000/40 = 200 shares
Initial margin 50%:    Put 50%* 8,000 = 4,000 in the margin account
Borrow amount:    (1- 50 %)* 8,000 = 4,000
At the time of purchase:
Stock        $ 8,000
Loan        $ 4,000
Equity        $ 4,000
After one year:
Stock        8,000/40 = 200P
Loan        (1- 50 %)* 8,000 = $ 4,000
Int. payable    4,000 * 6% = $ 240
Equity        200P-4,000-240

A margin call will occur if Equity/Market value = 0.30 or less
0.3 = (200P - 4,000 - 240)/200P
60P = 200P - 4,240
-140P = -4,420
P = $ 30.29

Answer B

To restore the 50% IMR, 50%*(200*30.29) = 3,029
Additional fund needed= 3,029 -(200*30.29- 4,000) = $ 971

Answer C

Investment Cost    8,000 * 50% = $ 4,000
Value of Stock in 1 yr     200 * 30.29 = $ 6,058
Interest Due         $ 240
Loan          $ 4,000
Net Profit        $ 1,818

Return = (Net profit/Investment Cost -1) * 100
Return = ((1,818/4,000)-1) * 100 = -54.55%