Question

Carlos buys 100 shares of IBM for $100 per share on 50% margin.

a) How much money does Carlos need to give to his broker, and how much money does he borrow?

b) If IBM goes up to $120 per share, how many more shares could Carlos sell without sending his broker more money?

c) If IBM goes down to $80 per share, how much money does Carlos have to send his broker to get back to the 50% margin requirement?

d) Instead of sending his broker more money, Carlos sells some of his shares (at $80 per share) to get his account back to 50% margin. How many shares does he have to sell?

Answer 1

Buying on margin means the purchase of an asset by using leverage and borrowing the balance from a bank or a broker.

In the given case, Carlos buys 100 shares of IBM for $100 per share on 50% margin. That means Carlos paid only 50% for buying the shares and borrowed the remaining 50% from a broker.

Question (a): As it was mentioned Carlos buys shares on 50% margin. So the remaining 50% amount is borrowed from his broker.

Amount borrowed from the broker = total value of investment * 50% = (100 shares * $100) * 50%

Amount borrowed from the broker = $5000

Therefore, the amount Carlos need to give to his broker = $5000

Question (b):

If IBM share price goes up to $120, then the total value of the shares = 100 shares * $120 = $12000

Since, Carlos bought $5000 from his broker on 50% margin, he can sell $2000 value of shares ($12000 - $10000).

Therefore, the no.of shares Carlos could sell without sending money to his broker = $2000/$120 = 16.66 shares

Therefore, the no.of shares Carlos could sell without sending money to his broker = 16 shares (approx.)

Question (c):

If IBM share price goes down to $80, then the total value of the shares = 100 shares * $80 = $8000

Since, Carlos bought $5000 from his broker and the value of the shares are still at $8000, Carlos need to send $2000 to his broker to get back to the 50% margin.

Question (d):

Margin requirement = 50%

The value of the shares = 100 shares * $80 = $8000

Let's assume that the amount required to be sold is A.

Margin requirement = (Borrowed amount - A) / (value of shares - A)

50% = ($5000 - A) / ($8000 - A)

50% * ($8000 - A) = $5000 - A

$4000 - 0.5A = $5000 - A

A - 0.5A = $5000 - $4000

0.5A = $1000

A = $1000/ 0.5 = $2000

The value of the shares required to be sold = $2000

Therefore, the shares required to be sold to get the 50% margin = $2000/ $80 = 25 shares

Verification of margin percentage after selling 25 shares:

Remaining shares = 75

Value of the shares at $80 per share = 75 * $80 = $6000

Remaining amount borrowed from the broker = original $5000 - repaid $2000 = $3000

Margin = borrowed amount/ stock value = $3000/ $6000 = 50%