An investor buys 1,000 shares of a non-dividend-paying stock for $18. The initial margin requirement is 40% and the maintenance margin is 30%. After one year the investor sells the stock for $24 per share. The investor's rate of return on this investment (ignoring borrowing and transactions costs and taxes), and the price at which the investor would receive a margin call, are closest to:
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Rate of return |
Margin call |
To obtain the result:
Part 1: Calculate Margin Return:
Margin Return % = [((Ending Value - Loan Payoff) / Beginning Equity Position) – 1] * 100 =
= [(([$24 × 1,000] – [$18 × 1,000 × 0.60]) / ($18 × 0.40 × 1,000)) – 1] × 100 =
= 83.33%
Alternative (Check): Calculate the all cash return and multiply by the margin leverage factor.
= [(24,000 – 18,000)/18,000] × [1 / 0.40] = 33.33% × 2.5 = 83.33%
Part 2: Calculate Margin Call Price:
Since the investor is long (purchased the stock), the formula for the margin call price is:
Margin Call = (original price) × (1 – initial margin) / (1 – maintenance margin)
= $18 × (1 – 0.40) / (1 – 0.30) = $15.43
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