Is there an exact percentage drop for a stock for it to trigger a margin call?

Traditionally, Reg T margin for long purchases is 50% and the margin maintenance requirement (MMR) is 25%. Brokers can require more margin and some who previously were at the Reg T limit raised it before the election due to the expectation of volatility (some raised it this week but AFAIK, just for a limited number of stocks).

Your guess of $71.42857142857143 per share is correct (an account value of $142.8572... ) for a MMR of 30%.

For margin calculations, as account value drops, your equity drops the same amount (the debit remains the same), resulting in a decrease in margin:

 Market Value   Debit   Equity  Margin %
      200        100     100     50.00%
      180        100      80     44.44%
      160        100      60     37.50%
      142.86     100      43     30.00%

The short cut formula is for determining the market level at which the account will hit the 30% MMR is 10/7 times the debit balance which in your example is $142.86 or $71.43 per share.

To calculate the exact percentage drop for a stock for it to trigger a margin call, you would subtract the share price where the MMR is reached from the cost per share of the position and divide by the cost per share of the position. This calculation is for a long position on 50% margin. It will not work for a different amount of initial margin.

The equity at that level would be the market value less the debit value.

I wanted to add the method I use and the equation here as formatted by MathJax, but looks like unlike Stack Exchange Physics , MathJax cannot be used, so here is plain text equation version:

I am just using a stock that is $1, and we borrow $1 from the brokerage to buy another share for $1. x is the amount of price drop:

(1 - 2x) / (2 - 2x) = 30%

(1 - 2x) / (2 - 2x) = 0.3      # now multiply both sides by (2 - 2x)

(1 - 2x) = 0.3 (2 - 2x)

1 - 2x = 0.6 - 0.6x

1 - 0.6 = 2x - 0.6x

0.4 = 1.4x

x = 0.4 / 1.4

x = 0.28571428571428575

So that means, when the price of the stock drops by roughly $0.2857, or 28.57%, then it is at the 30% margin requirement border, and if it drops slightly after that, then it will be a margin call.

To verify, if the stock drops by $0.2857, then how much "equity" or value do we have?

$1 - ($0.2857 × 2) = $0.4286

And what about the value of the whole investment?

$2 - ($0.2857 × 2) = $1.4285999999999999

So if we divide 0.4286 by 1.4285999999999999, we indeed get 0.3000139997200056, which is about 30%.