You sold short 100 shares of common stock at $75 per share. The initial margin is 50%. At what stock price would you receive a margin call if the maintenance margin is 30%?

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When you sell short, the initial transaction involves selling shares you do not own, with the intention of buying them back later at a lower price. The initial margin requirement of 50% means you must have half the value of the short sale in your account, which in this case is 100 shares at $75 each, totaling $7,500. Therefore, you need $3,750 in your account initially (50% of $7,500).The maintenance margin is the minimum amount of equity that must be maintained in the margin account after the stock is sold short, which in this case is 30%. To find the stock price at which you would receive a margin call, you can use the formula for the value of the equity in the account after a price change, which must be equal to or greater than the maintenance margin requirement.Let P be the price at which a margin call occurs. The total value of the short position at this new price is 100P. The equity in the account is the initial value of the short sale ($7,500) minus the increase in the value of the short position (100P - $7,500). This equity must equal 30% of the value of the short position at the new price, or 0.30 * 100P.Setting up the equation:$$7,500 - (100P - 7,500) = 0.30 \times 100P$$Solving for P gives:$$15,000 - 100P = 30P$$$$130P = 15,000$$$$P = \frac{15,000}{130} = 115.38$$However, since the question asks for the price at which you would receive a margin call, and none of the provided options match the calculated result, it seems there was a mistake in my calculation process based on the provided options. Let's correct the approach considering the correct method to calculate the price at which a margin call occurs for a short sale:For a short sale, the formula to determine the price at which a margin call occurs considering the maintenance margin (MM) is:$$ \text{Equity} = \text{Initial Value} - \text{Current Value} = \text{MM} \times \text{Current Value} $$Given the initial sale is 100 shares at $75, the initial value is $7,500, and the initial margin is 50%, leading to an initial equity of $3,750. The maintenance margin is 30%. The correct approach to find the price at which a margin call occurs is:$$ \text{Equity} = \text{Initial Sale} - \text{Number of Shares} \times \text{New Price} $$$$ \text{Equity} = 7,500 - 100P $$This equity needs to be 30% of the current value of the position:$$ 7,500 - 100P = 0.30 \times 100P $$$$ 7,500 = 130P $$$$ P = \frac{7,500}{130} $$This calculation was intended to find the correct price P at which a margin call occurs, but it seems there was a misunderstanding in the application of the formula. The correct calculation directly addresses the relationship between the price increase, the equity in the account, and the maintenance margin requirement for a short sale. Given the options and the mistake in the calculation, let's correct the approach based on the standard formula for a margin call in a short sale scenario:$$ \text{Margin Call Price} = \text{Initial Price} \times \left(1 + \frac{\text{Initial Margin Requirement}}{1 - \text{Maintenance Margin Requirement}}\right) $$Using the correct formula and values:$$ \text{Margin Call Price} = 75 \times \left(1 + \frac{0.50}{1 - 0.30}\right) $$This formula correctly calculates the price at which the equity in the account falls to the maintenance margin level, necessitating a margin call. However, the initial explanation attempted to directly solve for the price without correctly applying the formula specific to short sales and margin calls. The correct answer should be derived from understanding the relationship between the sale price, margin requirements, and how they affect the price at which a margin call is triggered. Given the mistake in the initial calculation and explanation, the focus should be on correctly applying the principles of margin requirements in short selling to find the accurate stock price for a margin call, which should align with one of the provided choices.

You Sold Short 100 Shares of Common Stock at $75