Question

You have just borrowed $67,500 on margin to buy shares in ABC, which is currently quoting as the bid price of $29.99 bid and the ask price of $30.00 ask per share. The minimum margin is 35%, and your initial margin requirement is 55%. Assume that ABC will pay no dividends before you return the loan and that that you pay no interest on your loan.

1. If you buy ABC in margin, what is the maximum number of shares you can buy?
2. Suppose you bought the maximum number of shares of ABC as in (1).
   1. Assume that immediately after your purchase, ABC’s share price drops to $26.00 per share. Calculate your new margin. Will you receive a margin call?
   2. What is the maximum price at which you will receive a margin call?
   3. If the stock price falls to $20, you would get a margin call. If that happens, how much in additional funds would you need to add to your account to respond to the margin cal

Hints:

• New fund needed = Original loan – Maximum Loan given market value
• Maximum loan = (1 – minimum margin) (Market value of shares
• When margin call occurs, the margin balance is bumped up to the minimum (maintenance) margin.

Answer 1

	Maximum number of shares of ABC that can be purchased = 67500/(55%*30) =	4091
a)	New margin = 4091*26*35% =	$37228
	Balance in margin account = 67500-(30-26)*4091 =	$51136
	As the balance in the margin account is more than the new
	margin required, no margin call will be received.
b)	Maximum price for which no margin call will be required =
	67500-(30-p)*4091 = 4091*35%*p, where p is the new price
	Solving for p
	67500-122730+4091*p = 1431.85*p
	55230 = 2659.15*p
	p = 55230/2659.15 = $20.77
c)	New margin required = 4091*20*35% =	$28637
	Balance in margin account = 67500-(30-20)*4091 =	$26590
	Additional funds required	$2047