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Top Broker plc opens a brokerage account and short-sells 1,000 shares of XYZ stock at £20 per share
Top Broker plc opens a brokerage account and short-sells 1,000 shares of XYZ stock at £20 per share. The initial margin requirement is 50% and the maintenance margin is 30%. The price of the stock rises to £25 per share in the following year. The stock also pays dividend of £2 per share. Required: (a) What is the remaining margin in Top Broker's account at the end of the year? (5 marks) (b) Will Top Broker receive a margin call? (1 mark) (c) What is the company's return on investment? (5 marks) (d) What is the maximum price of the stock such that Top Broker has exactly 30% margin in year 1? (9 marks) (Total: 20 marks)
Expert Solution
a)
Initial Price = 20
Number of Shares = 1,000
Value of shares shorted = 20 x 1,000 = 20,000
Margin = 50%
Equity in the account = 50% x 20,000 = 10,000
Total value of the account = 10,000 + 20,000 = 30,000
Total dividends paid = 2 x 1000 = 2,000
When the share price is 25, value of the shares shorted = 25 x 1000 = 25,000
Margin = (equity - dividends) / Value of shorted shares = (10,000 - 2,000) / 25,000 = 32%
b)
Since the margin is above the maintenance margin of 30%, the company will not receive a margin call.
c)
Rate of return = (Sale price - Dividend per share - Purchase Price) x shares / Initial Margin = (20 - 2 - 25) x 1000 / 10,000 = -70%
d)
Margin = (equity - dividends) / Value of shorted shares
30% = (10,000 - 2,000) / Value of Shorted Shares
Value of Shorted Shares = 8,000 / 0.3 = 26,666.67
Share price at 30% margin x 1,000 = 26,666.67
Share price at 30% margin = 26.67
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