Final answer:
The price that would trigger a margin call is $150 per share. The stock price that would allow the trader to withdraw $2,000 while maintaining a margin ratio above 50% is $90 per share.
Step-by-step explanation:
A trader has a margin account with a total cash deposit of $20,000 and bought 400 shares of a stock at the price of $100 each. To calculate the price of the stock that would lead to a margin call on this account, given a minimum margin maintenance of 25%, we need to know when the equity in the account falls to 25% of the market value of the stock. The initial value of the stock is 400 shares × $100 = $40,000. The trader has $20,000 equity (half of the value), so a margin call occurs when the trader's equity is 25% of the stock's current market value. This means 0.25 × Current Market Value = Equity after a decline in stock price.
To find the Current Market Value (CMV) that triggers a margin call:
Equity = $20,000 × (1 - Decline %)
0.25 × CMV = $20,000 × (1 - Decline %)
CMV = 4 × $20,000 × (1 - Decline %)
CMV = $80,000 × (1 - Decline %)
The trader owns 400 shares, thus:
$80,000 × (1 - Decline %) ÷ 400 = Price per Share after Decline
Solving for 'Decline %' when the account faces a margin call:
$80,000 - (400 × Current Price per Share) = $20,000
400 × Current Price per Share = $60,000
Current Price per Share = $150
For the stock price that would allow the trader to withdraw $2,000 while keeping the margin ratio above 50%:
Equity after withdrawal = $20,000 - $2,000
New Margin Ratio = Equity after withdrawal / CMV
$18,000 / CMV = 0.50
CMV = $36,000
$36,000 / 400 shares = $90 per share