Chris sells a stock short for a price of $80. The stock pays a dividend of $5. T

Question

Chris sells a stock short for a price of $80. The stock pays a dividend of $5. The margin requirement is 60% of the short sale price. The margin account earns an annual rate of 6%. The stock is purchased in one year for a price of X 9. Terry sells a different stock short for a price of $90. The stock pays no dividends. The margin requirement is 50% of the short sale price. The margin account earns an annual rate of 6%. The stock is purchased in one year for a price of X (same price that Chris pays). Terry's rate of return is three times that of Chris' return. Find the price X'at which the purchase their respective stock

Explanation / Answer

Terry sells a stock at $90. Margin required is $45 (which will be kept in the margin account) Since annual rate is 6% and terry buys the stock at same price, rate of return on his money is 6%

Now Terry's rate of return is 3 times that of chris's return.

So Chris's rate of return is 2%

Now Chris sells at $80. Margin Required is 60%*80 = $48. Since you have shorted the stock, dividend income will not be yours and so it has no effect on Chris's rate of return. Now the margin account earns 6%. But we know total return is 2%. Which means, total value at the end of 1 year is 48*1.02 = $48.96

Now Since margin account gives 6% return, ending value is 48*1.06 = $50.88. So loss in short sale position is 50.88-48.96 = $1.92.

Since 1.92 is the loss amount, the stock must have been purchased at $80+$1.92 = $81.92

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