Explanation

To find the stock price at which a margin call occurs, we need to calculate the maintenance margin price.

Step 1: Calculate initial investment and loan amount

• Total purchase value = 500 shares × $36 = $18,000
• Initial leverage ratio = 1.66
• Leverage ratio = Total assets / Equity
• 1.66 = $18,000 / Equity
• Equity = $18,000 / 1.66 = $10,843.37
• Loan amount = Total purchase - Equity = $18,000 - $10,843.37 = $7,156.63

Step 2: Calculate maintenance margin price Maintenance margin requirement = 30%

Formula for margin call price: $P_m = \frac{L}{1 - MM}$ Where:

• $P_m$ = Margin call price per share
• $L$ = Loan per share
• $MM$ = Maintenance margin requirement

Loan per share = $7,156.63 / 500 shares = $14.31326

$P_m = \frac{14.31326}{1 - 0.30} = \frac{14.31326}{0.70} = 20.4475$

Wait, this gives $20.45, which doesn't match any options. Let me recalculate using the correct formula.

Step 3: Correct formula for margin call price The correct formula is: $P_m = \frac{L}{1 - MM} \times \frac{\text{Number of shares}}{\text{Number of shares}}$

Actually, let's use the equity formula: Equity = Market value - Loan Maintenance margin = Equity / Market value ≥ 30%

Let P = stock price at margin call Market value = 500P Equity = 500P - $7,156.63

Maintenance margin requirement: $\frac{500P - 7,156.63}{500P} ≥ 0.30$

$500P - 7,156.63 ≥ 0.30 × 500P$ $500P - 7,156.63 ≥ 150P$ $500P - 150P ≥ 7,156.63$ $350P ≥ 7,156.63$ $P ≥ \frac{7,156.63}{350}$ $P ≥ 20.4475$

This gives $20.45, which is closest to option A ($20.57). But let me check if I made an error.

Step 4: Alternative approach Initial margin = 1/1.66 = 60.24% Loan = 39.76% of $18,000 = $7,156.80

At margin call: Equity = 30% of market value Market value = 500P Equity = 500P - 7,156.80

500P - 7,156.80 = 0.30 × 500P 500P - 7,156.80 = 150P 350P = 7,156.80 P = 20.4477

This confirms $20.45.

Step 5: Check the options The calculated value $20.45 is closest to option A ($20.57). However, there might be rounding differences or I might be using the wrong formula.

Let me check using the formula: P = Loan / (Number of shares × (1 - MM)) P = 7,156.63 / (500 × 0.70) = 7,156.63 / 350 = 20.4475

This confirms $20.45.

Given the options: A. $20.57 B. $25.20 C. $30.86

The calculated $20.45 is closest to A ($20.57).

Therefore, the correct answer is A.