Question

Suppose the Xenon (XO) currently is selling at $90 per share. You buy 300 shares, using $20,000 of your own money, and borrow the remainder of the purchase price from your

broker. The rate on the margin loan is 6 percent.

a. If the minimum margin is 30 percent, how low can XO’s price fall before you get a margin call?

b. How would your answer to (a) change if you had financed the initial purchase with only $15,000 of your own money?

Answer 1

a). Loan Amount = Value of Investment - Initial Margin

= ($90*300) - $20,000 = $27,000 - $20,000 = $7,000

Assume price be P

Value of 300 shares is 300P

Equity = Value of Shares - Borrowed Amount = 300P - $7,000

Required margin = Equity / The value of the shares

0.30 = [300P - $7,000] / 300P

0.30 * 300P = 300P - $7,000

90P = 300P - $7,000

300P - 90P = $7,000

210P = $7,000

P = $7,000 / 210 = $33.33

You will receive a margin call when the stock price falls below $33.33

b). Loan Amount = Value of Investment - Initial Margin

= ($90*300) - $15,000 = $27,000 - $15,000 = $12,000

Assume price be P

Value of 300 shares is 300P

Equity = Value of Shares - Borrowed Amount = 300P - $12,000

Required margin = Equity / The value of the shares

0.30 = [300P - $12,000] / 300P

0.30 * 300P = 300P - $12,000

90P = 300P - $12,000

300P - 90P = $12,000

210P = $12,000

P = $12,000 / 210 = $57.14

You will receive a margin call when the stock price falls below $57.14