Suppose that Intel currently is selling at $20.00 per share. You buy 1,000 share

Question

Suppose that Intel currently is selling at $20.00 per share. You buy 1,000 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%.

A) What is the percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to: (i) $22.00; (ii) $20.00; (iii) $18.00? What is the relationship between your percentage return and the percentage change in the price of Intel?

B) If the maintenance margin is 25%, how low can Intel’s price fall before you get a margin call?

C) How would your answer to question b change if you had financed the initial purchase with only $10,000 of your own money?

D) What is the rate of return on your margined position (assuming again that you invested $15,000 of your own money) if Intel is selling after one year at: (i) $22.00, (ii) $20.00, (iii) $18.00? What is the relationship between your percentage return and the percentage change in the price of Intel? Assume that Intel pays no dividends.

E)Continue to assume that a year has passed. How low can Intel’s price fall before you get a margin call?

Explanation / Answer

Answer:A) The value of the 1000 shares at the time of the purchase is $20,000 and thus $5,000 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. If the price of Intel stock jumps to p , say, the return on the investment, denoted rp, is given by:

rp=(p*1000-5000-15000)/15000

=(1000p-20000)/15000

Hence r22=13.33% ,r20=0% , r18=-13.33%

Let p= (1 +)20 denote the stock price following the jump, indicating the percentage change in the stock price. The return on the investment, given , is then given by:

r=[(1 +)20*1000-5000-15000]/15000

=[(1 +)20000-20000]/15000

Answer:B) For a price p , the margin ratio is

(1000p-5000)/1000p

Thus a margin ratio 0.25 implies that

(1000p-5000)/1000p=0.25

=250p=1000p-5000

p=6.67

Answer:C) In this case, the loan from the broker would be $10,000 and thus, for a price p , the margin ratio would be

(1000p-10000)/1000p

Thus a margin ratio 0.25 implies that

(1000p-10000)/1000p=0.25

=250p=1000p-10000

p=13.33

Answer:D) Let p denote the price of Intel's stock at the end of the year. The return on this investment, rp, is then

rp=(1000p-(1.08)5000-15000)/15000

=1000p-20400/15000

Hence r22=10.67% ,r20=-2.67% , r18=-16%

The relationship between the percent change in Intel’s stock price, , and the investor’s return is given by

r=1000(1 +)2020,400 /15,000

Answer:e For a price p, the margin ratio is then

1000p5,400/1000p.

Thus a margin ratio 0.25 implies that

1000p5,400/1000p=0.25

p=21.6

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