Explanation

To determine the price at which a margin call occurs, we need to calculate the maintenance margin requirement and find the stock price that triggers it.

Given:

• Initial deposit = $5,000
• Shares purchased = 300
• Purchase price = $30 per share
• Maintenance margin = 30%

Step 1: Calculate total purchase value Total purchase = 300 shares × $30/share = $9,000

Step 2: Calculate loan amount (margin borrowed) Loan amount = Total purchase - Initial deposit = $9,000 - $5,000 = $4,000

Step 3: Calculate equity when price changes Let P = stock price Equity = (300 × P) - $4,000 (market value minus loan)

Step 4: Maintenance margin formula Maintenance margin = Equity / Market value ≥ 30% Equity / (300 × P) ≥ 0.30

Step 5: Set up inequality (300P - 4000) / (300P) ≥ 0.30

Step 6: Solve for P 300P - 4000 ≥ 0.30 × 300P 300P - 4000 ≥ 90P 300P - 90P ≥ 4000 210P ≥ 4000 P ≥ 4000/210 P ≥ 19.0476

Step 7: Interpret result The maintenance margin requirement is satisfied when P ≥ $19.05. When P < $19.05, equity/market value < 30%, triggering a margin call.

Therefore, the price below which the investor will first receive a margin call is $19.05.

Verification: At P = $19.05:

• Market value = 300 × $19.05 = $5,715
• Equity = $5,715 - $4,000 = $1,715
• Equity ratio = $1,715 / $5,715 = 0.300 = 30% (exactly at maintenance margin)

At P = $19.04:

• Market value = 300 × $19.04 = $5,712
• Equity = $5,712 - $4,000 = $1,712
• Equity ratio = $1,712 / $5,712 = 0.2997 = 29.97% (< 30%, margin call)

Thus, Option A ($19.05) is correct.