Final answer:
The stock price at which a margin call would occur, given an initial $150 per share sale price, a 50% initial margin requirement and a 30% maintenance margin, is $173.08.
Step-by-step explanation:
In a short-selling scenario where a student sold 100 shares of stock at $150 per share with an initial margin requirement of 50%, and a maintenance margin of 30%, we can calculate at what stock price a margin call would occur by using the formula for the minimum account balance required to maintain the position (initially, this would be the sale price of the stocks plus the margin):
To find the stock price that would trigger a margin call, we need to determine when the margin account balance falls to a point where it's only 30% of the short position (the value of the shares that were short-sold). We use the balance equation:
Equity = Total account value - Short position value
Maintenance margin = Equity / Short position value > 30%
For a margin call to occur:
Total account value - Short position value = Short position value × 30%
Total account value = 1.3 × Short position value
Since the Total account value is fixed at $22,500, we can find the Short position value at margin call:
$22,500 = 1.3 × Short position value
Short position value at margin call = $22,500 / 1.3
Short position value at margin call = $17,307.69
Dividing this by the number of shares gives us the price per share at margin call:
Stock price at margin call = Short position value at margin call / Number of shares
Stock price at margin call = $17,307.69 / 100 shares
Stock price at margin call = $173.08