About margin call

[zjqadele]

I can really be able to figure out how to get the price when the margin call first occurs…
The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If the maintenance margin is 30 percent, at what price will a margin call first occur?
(Level I 2012 Volume 5 Equity and Fixed Income, 7th Edition. Pearson Learning Solutions p. 75).

 

[samc]

To pay back loan s/he needs to pay back half the purchase price i.e. $12.5 per share.
So the amount going to him/her per share sold is p-12.5
Now we need the proportion going to him i.e. (p-12.5)/p to equal 0.3. So solve (p-12.5)/p=0.3. This gives p=12.5/0.7 = $17.86

 

[iossif]

Margin Requirement = 0.50 ($10,000 from $20,000 invested is a loan)
Maintenance Margin = 0.30
Margin Call occurs at P = 25 x ((1 - 0.50)/(1 - 0.30)) = $17.86
If you can’t memorize the formula, just remember that in a long position, your margin call always occurs at a lower price, so you need to multiply the current price by a ratio < 1 using (1 - margin requirement %) and (1 - maintenance margin %). It’s as simple as that.
Hope that helps.