Justin just made a margin purchase of 100 shares of DEF Corp. for $22.50 per share. The initial ...

$9.64

Excerpt

To determine how low the price of each share of DEF can go before Justin has to add equity to his account, you can use the formula for the minimum equity requirement in a margin purchase:

Minimum Equity Requirement = (Total Value of Investment) - (Borrowed Amount) = (Number of Shares * Price per Share) - (Initial Margin Requirement * Number of Shares)

Let's calculate it step by step:

Number of shares = 100
Price per share = $22.50
Initial Margin Requirement = 70% (0.70)
Now, calculate the Total Value of Investment:

Total Value of Investment = Number of Shares * Price per Share
Total Value of Investment = 100 * $22.50 = $2,250

Next, calculate the Borrowed Amount:

Borrowed Amount = Total Value of Investment - Equity
Borrowed Amount = $2,250 - (Initial Margin Requirement * Total Value of Investment)
Borrowed Amount = $2,250 - (0.70 * $2,250)
Borrowed Amount = $2,250 - $1,575
Borrowed Amount = $675

Now, we have the borrowed amount, and we want to find the lowest share price at which Justin will have to add equity. To do this, we'll calculate the equity level that corresponds to the maintenance margin requirement of 30% (0.30):

Equity at Maintenance Margin = Total Value of Investment * Maintenance Margin Requirement
Equity at Maintenance Margin = $2,250 * 0.30
Equity at Maintenance Margin = $675

Now, Justin will have to add equity when the equity in his account drops to $675. To find out the lowest share price, we can use this equity level:

Equity at Maintenance Margin = (Number of Shares * Price per Share) - (Maintenance Margin Requirement * Number of Shares * Price per Share)

$675 = (100 * Price per Share) - (0.30 * 100 * Price per Share)

Now, solve for the Price per Share:

$675 = 100 * Price per Share - 0.30 * 100 * Price per Share
$675 = 100 * Price per Share * (1 - 0.30)

Now, divide both sides by 100 * (1 - 0.30):

Price per Share = $675 / (100 * (1 - 0.30))
Price per Share = $675 / (100 * 0.70)
Price per Share = $675 / $70
Price per Share ≈ $9.64

So, the lowest price per share of DEF Corp. before Justin will have to add equity to his account is approximately $9.64.

The correct answer is:

▸ $9.64

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Justin just made a margin purchase of 100 shares of DEF Corp. for $22.50 per share. The initial ...

Fundamentals of Investing

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