Suppose you sold short $3000$ shares at a price of $$50$ per share. The margin requirement is $60\%$ and the maintenance margin is $25\%.$ The brokerage cost is $1\%$ of the value of stocks sold short.

Proceeds from short sale $=3000$$$50-3000$$$500\mathrm{.}01=$$$148,500$

Margin requirement $=0\mathrm{.}6$$$503000=$$$90000$

The total amount $$238,500($$$148500+$$$90000)$ will be held in a safe account that you cannot touch until you cover your position $($buy and return the stocks to the brokerage house$).$ This amount $($$$238,500)$ is your asset. Your liability is the amount you have to come up with to buy back $3000$ shares you sold short. What is the critical price $($P$)$ at which you will get a margin call?

$0\mathrm{.}25=\frac{E}{V}$alue $of$ stocks sold short

$,=\frac{\text{\$}238,500-3000P}{3000P}$

$0\mathrm{.}25(3000P)=$$$238,500-3000P$

$750P=$$$238,500-3000P$

$3750P=$$$238,500$

$P=$$$238,\frac{500}{3750}=$$$63\mathrm{.}6$

If the stock price goes up to $$63\mathrm{.}6$ or higher, you will get a margin call.

Homework: Now assume that the stock has paid a year$-$end dividend of $$3$ per share and you still have a short position in the stock. What would be the critical price at which you would get a margin call? $$61\mathrm{.}20$