Question

Kurt opens a trading account with $29,100 on September 25, and purchases 1,200 shares of TPHB stock at $48.50 per share. The account has a 50% initial margin requirement and a 40% maintenance margin requirement.  

a. What is the highest price of TPHB at which Kurt will get a margin call?

b. Suppose that the price of TPHB slowly declines to close at $42.60 on November 30. On December 1, the stock declines dramatically from $42.60 to $36.80. What will be the value of Kurt's margin call?

c. What will be the value of Kurt's equity in his trading account on December 1 after he meets his margin call?

d. Suppose that instead of meeting his margin call, Kurt decides to sell all of his shares of TPHB. What is the return on his investment?

Answer 1

a. Margin Call Price = Initial Purchase Price * { (1 - initial margin ) / ( 1 - maintenance margin ) }

= $48.50 * { ( 1 - 0.50 ) / ( 1 - 0.40 ) }

= $48.50 * ( 0.50 / 0.60 )

= $48.50 * 0.833

= $40.40

$40.40 is the highest price of TPHB at which Kurt will get Margin Call. Kurt receives a margin call if the price of the shares goes below $40.40.

b. Kurt purchase 1200 shares at $48.50. i.e., $58,200 out of which $29,100 is initial margin (50%) , that means Kurt is using $29,100 as his money or his equity and remaining $29,100 is borrowing from broker. Maintenance margin is 40%, it means Kurt’s own money must comprise at least 40% of the share's value.

Stock declines to $36.80 on December 1. So the account value is $44,160 ( 1200 shares * $36.80 )

Broker's borrowing value not change it remains $29,100

Now Kurt's equity is $15,060 ( $44,160 - $29,100 )

So, Equity percentage is ( $15,060 / $44,160 ) * 100 = 34.10% , which is below 40% of maintenance margin.

Formula used to calculate the need to meet the maintenance margin on a margin call:

Cash Deposit to Meet Maintenance Margin = (Market Value of Shares * Maintenance Margin) – Investor’s New Equity

= ( $44,160 * 0.40 ) - $15,060

= $2,604

Kurt's receive a margin call to deposit $2,604 by the due date.

c. Kurt's equity in his trading account on December 1 after he meets his margin call = $15,060 + $2,604 = $17,664

d. As Kurt's equity at the time of investment is only $29,100 and on December 1 his equity is $15,060

so return on investment = { ($15,060 - $29,100) / $29,100 } * 100 = -48.25%