Final answer:
Michelle would receive a margin call when the price of Apple shares reaches $132.00, as this is the point where the equity in her account would fall to the 40% maintenance margin requirement.
Step-by-step explanation:
To determine at what Apple share price Michelle would receive a margin call from her broker Fidelity after doing a short sale of 1000 Apple stock at a price of $110, we need to calculate the price at which the equity in her account falls to the maintenance margin requirement of 40%. The initial margin requirement was 60%, so Michelle initially had an equity position of 60% of the value of the short sale.
Let's denote P as the unknown price at which a margin call occurs. Since Michelle short-sold the stock, a rise in the stock's price reduces her equity. The equity in the account when a margin call occurs is the initial equity minus the increase in the value of the 1000 shares, which can be represented as:
Equity = (Initial Margin Requirement * Value of Short Sale) - (1000 * (P - Initial Price))
The maintenance margin occurs when this equity equals 40% times the current market value of the short position, which is:
Maintenance Margin = 0.40 * (1000 * P)
At the point of margin call, Equity = Maintenance Margin. So, we solve the following equation:
(0.60 * 1000 * $110) - (1000 * (P - $110)) = 0.40 * (1000 * P)
After solving, we find that the price P at which a margin call is received is $132.00 per share. At this price, the increase in the value of the short sold shares reduces Michelle's equity to the point where it exactly matches the maintenance margin requirement.