4. Suppose that AOL is selling at $26 per share. You buy 1000 shares using $20,0

Question

4. Suppose that AOL is selling at $26 per share. You buy 1000 shares using $20,000 of your own money and borrow the remainder of the purchasing price from you broker. The rate on the margin loan if 7%. AOL does not pay any dividends.

a. What is the percentage increase in the net worth of your brokerage account if the price of AOL immediately changes to (i) $30; (ii) $26; (iii) $22?

b. If the maintenance margin is 20%, how low can AOL’s price fall before you get a margin call?

c. What is the rate of return on your margined position (assuming again that you invest $20,000 of your own money) if AOL is selling after one year at (i) $30; (ii) $26; (iii) $22?

Explanation / Answer

The value of 1000 shares at the time of purchase is $26,000 and hence $6,000 had to be borrowed from the broker. With an immediate price change, we don’t need to worry about the interest rate on the loan.

a. percentage increase in net worth

(i) (30*1000-20000-6000)/20000= 4000/20000= 20%

(ii) (26*1000-20000-6000)/20000= -

(iii)(22*1000-20000-6000)/20000= -4000/20000= -20%

b. For a price p, the margin ratio is

(1000p 6, 000) /1000p .

Thus a margin ratio 0.20 implies that

(1000p 6, 000) /1000p = 0.20 = 1000p 6, 000 = 200p = p = 6, 000 /800 = . 7.5

c.

percentage increase in margined position

(i) (30*1000-20000-6000(1.07))/20000= 3580/20000= 17.9%

(ii) (26*1000-20000-6001.07))/20000= -420/20000=-2.1%

(iii)(22*1000-20000-6000(1.07))/20000= -4420/20000= -22.1%

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