Question

I am studying for Investments 10th by Bodie Kane in my University.
As doing assignments, I have these questions concerning margin problems. Could any experts help me to solve these questions?:)

Rachel opens a margin account and purchases 400 shares of Ross Inc. at $40 per share. The initial margin requirement is 50%. The share price falls to $25 per share by the end of the year.
1) What is the remaining margin in the account?
2) If the maintenance margin requirement is 30%, will she receive a margin call?
3) How much will she have to put up to get back to 50% when her broker calls?
4) If she does not have any more cash, how many shares she has to sell to pay back the broker?
5) If price increases to $50 per share by the end of the year instead, how many more shares she can buy by borrowing more from her broker?

Answer 1

Solution:

Margin account purchase of shares is $16,000 (400 shares*$40)

Her initial Margin required is 50% i.e $8,000 ($16,000*0.5)

At the end of year share price fell to $25, so her share value is $10,000 (400 shares * $25)

1) Remaining margin in the account is $2,000 ($10,000-$8,000)

2) Yes, because she had $16,000 worth of securities bought using $8,000 in cash and $8,000 on margin. Now the total value of her holding is dropped to $10,000 and the amount she borrowed on margin remains $8,000, her equity worth will only be $2,000, which falls below the 30% (30% of cash is $2,400 i.e 30% Maintainance margin *$8,000 cash requirement) minimum margin requirement.

3) She has to put back $6,000 (Original stock vale with 50% margin $16,000 - Current stock value $10,000)

4) She has to sell 54 share worth $1,350

After shares sale initial margin will be $6,650 & her cash purcahse will be $2,000, calculation is explained below

Her current cash balance - $2,000

So with her $2,000 she has to maintain 30% margin ($2,000/30)*100 is 6,667

$8,000 - 6,667 = $1,333

$1,333/$25 = 53.32 shares need to be sold

5) She can purchase 80 shares worth $4,000

Her original investment $8,000

Her current investment value (cash) is $12,000 ($50*400-$8000 margin)

She can hold stock double the cash she has = $12,000/0.5

So $24,000-$20,000 = $4,000