Suppose that Xtel currently is selling at $50 per share. You buy 500 shares using $17,500 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 Xtel immediately changes to (i) $56; (ii) $50; (iii) $44?

b. If the maintenance margin is 30%, how low can Xtel's price fall before you get a margin call?

c. How would your answer to (b) would change if you had financed the initial purchase with only $12,500 of your own money?

d. What is the rate of return on your margined position (assuming again that you invest $17,500 of your own money) if Xtel is selling after one year at (i) $56; (ii) $50; (iii) $44?

e. Continue to assume that a year has passed. How low can Xtel's price fall before you get a margin call?


Answer 1


The value of the 500 shares at the time of the purchase is $25,000 therefore $7500 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 Xtel stock jumps to p, say, the return on the investment, denoted rp, is given


Explanation:.A) rp =

p × 500−7,500−17,500/17,500


500p − 25, 000/15, 000

Hence: r56 =500(56)-25,000/15,000= 28000-25,000/15,000 =20%


= 500(50)-25,000/15,000= 25,000-25,000/15,000= 0%

r44 = 500(44)-25,000/15,000= 22,000-25,000/15,000= -20%

B) For a price p, the margin ratio is

500p − 7,500/500p

A margin ratio 0.3 implies that

500p − 7,500/500p= 0.3=>500p − 7,500=150p

=>p= 7500/350= 21.43

C)For a price p, the margin ratio is

500p − 12,500/500p

A margin ratio 0.3 implies that

500p − 12,500/500p= 0.3=>500p − 12,500=150p

=>p= 12,500/350= 35.71

D). Let p denote the price of Xtel’s stock at the end of the year. The return on this investment, rp, is then

rp =500p − (1.08)7,500 − 17,500/17,500=

500p − 25, 400/17,500

Thus r56= 500(56)-25,400/17,500= 14.86%

r50 = 500(50)-25,400/17,500 = -2.29


r44= 500(44)-25,400/17,500= -19.43%

E) For a price p, the margin ratio is then

500p − 7,900/500p

Thus a margin ratio 0.3

implies that;

500p − 5,900/500p

= 0.3 => 500p − 5,900 = 150p

=> p = 5,900/350

= 16.86

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