Answer: $30.86

## 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.**

Author: LeetQuiz .