An investor purchased a stock for $60 a share using margin from his broken If the initial margin requirement is 40%, and the maintenance margin requirement is
20%, which of the following best describes the price at which a margin call will initially be triggered?
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A. B. C.B
To determine the price at which a margin call will initially be triggered, we need to understand the concepts of initial margin requirement and maintenance margin requirement.
The initial margin requirement is the minimum percentage of the total purchase price of a security that an investor must pay with their own funds. In this case, the initial margin requirement is stated as 40%. This means the investor must pay 40% of the stock's purchase price using their own money, while the remaining 60% can be borrowed from the broker.
The maintenance margin requirement is the minimum percentage of the total market value of the securities held in a margin account that must be maintained by the investor. If the value of the securities falls below this level, the investor will receive a margin call from the broker, requiring them to either deposit additional funds or sell securities to bring the account back to the required level. In this case, the maintenance margin requirement is stated as 20%.
Now let's calculate the price at which a margin call will initially be triggered.
The investor purchased the stock for $60 a share using margin. The initial margin requirement is 40%, so the investor needs to pay 40% of the purchase price using their own funds. This can be calculated as:
40% of $60 = 0.4 * $60 = $24
Therefore, the investor initially paid $24 using their own funds, and the remaining $36 ($60 - $24) was borrowed from the broker.
Now, let's calculate the price at which the market value of the securities held in the margin account would fall below the maintenance margin requirement.
The maintenance margin requirement is 20%. To calculate the market value at which a margin call will be triggered, we need to determine the price at which the equity (market value minus borrowed funds) falls below 20% of the market value.
Let's assume the market price of the stock is P. The market value of the securities is then calculated as:
Market value = Number of shares * Price per share = 1 * P (since the investor purchased 1 share)
The equity is calculated as the market value minus the borrowed funds:
Equity = Market value - Borrowed funds = 1 * P - $36
To find the price at which the equity falls below the maintenance margin requirement (20%), we set up the equation:
Equity / Market value < 20%
(1 * P - $36) / (1 * P) < 0.20
Simplifying the equation:
(1 * P - $36) / (1 * P) < 0.20 P - $36 < 0.20P $36 > 0.80P $36 / 0.80 > P $45 > P
Therefore, the price at which a margin call will initially be triggered is below $45.
The correct answer is B. Below $45.