Explanation

To determine the price at which a margin call will be received, we need to calculate the maintenance margin requirement price.

Step 1: Calculate the initial purchase details

• Purchase price per share = $30
• Number of shares = 300
• Total purchase value = 300 × $30 = $9,000
• Initial deposit (equity) = $5,000
• Amount borrowed (loan) = $9,000 - $5,000 = $4,000

Step 2: Set up the maintenance margin formula The maintenance margin requirement is 30%, which means:

Equity / Market Value ≥ 30%

Where:

• Equity = Market Value - Loan
• Market Value = Price per share × 300 shares
• Loan = $4,000 (constant, ignoring interest)

Step 3: Set up the inequality (Market Value - $4,000) / Market Value ≥ 0.30

Let P = price per share, then Market Value = 300P

(300P - $4,000) / (300P) ≥ 0.30

Step 4: Solve for P 300P - $4,000 ≥ 0.30 × 300P 300P - $4,000 ≥ 90P 300P - 90P ≥ $4,000 210P ≥ $4,000 P ≥ $4,000 / 210 P ≥ $19.0476 ≈ $19.05

Step 5: Interpret the result The investor will receive a margin call when the price falls below $19.05.

Verification:

• At P = $19.05: Market Value = 300 × $19.05 = $5,715 Equity = $5,715 - $4,000 = $1,715 Equity % = $1,715 / $5,715 = 30.0% (exactly at maintenance margin)
• At P = $19.00: Market Value = $5,700 Equity = $5,700 - $4,000 = $1,700 Equity % = $1,700 / $5,700 = 29.82% (below 30%, margin call triggered)

Therefore, the correct answer is A. $19.05.