Question

Your Margin account have $400 in cash. Price of the stock is $10 per share. Earlier bought a stock with 50% margin allowed by your broker, and use full margin. The 50% margin: 80 shares can be purchase and $800 is value of your account after the purchase. Now, suppose the broker issues margin call if margin % fall to 25%. The 25% margin: 160 shares can be purchase and $300 is value of your account after the purchase.

What will be the price of the stock then?

Answer 1

Solution:

Initial margin requirement is minimum amount required to open a position in stock exchange.

Maintenance margin requirement or Minimum margin requirement is minimum amount required to keep the position open and its generally lower than initial margin to work as a safety valve for clients. If this minimum margin is broken then client get Margin call to replenish their down position. Otherwise their position get closed.

Cash available in margin account = $400

Price of the stock = $10/ Share

Margin allowed by broker = 50% (Initial margin requirement)

with 50% margin share purchased = 80 shares

so, value of the purchase = $800

Margin call = 25% (Maintenance margin requirement)

Therefore, amount borrowed or leveraged = value of the purchase x (100% - Initial margin requirement)

So, Amount borrowed or leveraged = $800 x (100% - 50%)

= $800 x 50%

= $400

Calculation of the stock price:

Assume, Stock price = P

for stock price P value of the share will be 80P

Formula: (Value of the stock - Amount borrowed)/ value of the stock = Margin call

Putting value in the above formula we get,

(80P-$400)/80P = 0.25

80P-$400 = 20P

80P-20P = $400

60P= $400

P= $6.667/ share

Alternatively,

Formula: P = P₀ X (1- initial margin requirement)/(1-Maintenance margin requirement)

where P₀ is Stock price, P = Stock price

So, P = $10 X (1-0.50)/(1-0.25)

= $10 X 0.50/0.75

= $6.667/ share

So, Stock price will be $6.667 or $6.67per share.