Margin Call Price

My CFA notes provide the following formula for the price "c" which a margin call will occur for a long position in a stock, assuming the initial margin of "i", minimum margin of "m", and initial stock price of "p"

1 - i c = p * ----- 1 - m For example if you buy a stock at $40, have an initial margin of 40% and and the minimum margin of 25%, your margin call will occur at: $40 * ((1 - .4) / (1 - .25)) = $32 That's not at all an intuitive number to me and the formula seems weird either. 1-.25 is .75, what does it have to do with it? The formula becomes a little nicer when rearranged: c(1-m) = p(1-i) The right side of the equation represents the size of the loan. For example, the margin of 40% means i borrowed 60% (i.e. 1-40%). If the initial price of the stock was $40, the amount I borrowed was $40*60% = $24. p=(1-i) captures this relationship (i.e. $24=$40*(1-40%)) If the formula were c = p(1-i), c would be the price at which the value of the entire position would equal the size of the loan. So in the example, c would be $24. If the stock hit $24 and I sold off my position, I would have just enough to pay back what I borrowed. The -i part represents that the stock has lost the percentage of its price that I had paid out of pocket. Of course this means the stock must be sold off immediately since any further down move means that selling the position will not generate enough cash to pay back the loan. That's why the left side of the formula is actually c(1-m). If the minimum margin is 25%, 1-m is 75% and the margin call would be triggered at a price where 75% of the proceeds could cover the loan. This basically means that we have a margin of 25% that the price can drop after the margin call and still be sufficient to pay off the loan. To complete the example, if my loan is $24 then obviously that's the price at which the position can still cover the loan if sold. But the margin call will happen at $32, 6 dollars higher. $6/$24 = 25% which is our minimum (a.k.a maintenance) margin. To summarize, the margin call price is the price "m" percent above the price at which the value of the position equals the size of the loan, where m in the minimum margin. Similar logic applies for short selling except the minuses become plusses. 1 + i c = p * ----- 1 + m