Question

Suppose the Xenon (XO) currently is selling at $90 per share. You buy 300 shares, using $20,000 of your own money, and borrow the remainder of the purchase price from your

broker. The rate on the margin loan is 6 percent.

a. What is the percentage increase in the net wealth of your brokerage account if the price of XO immediately changes to

(1)$98

(2)$90

(3)$82

What is the relationship between your percentage return and the percentage change in the price of XO (derive the formula in general terms, not only the numbers)?

b. If the minimum margin is 30 percent, how low can XO’s price fall before you get a margin call?

c. How would your answer to (b) change if you had financed the initial purchase with only $15,000 of your own money?

d. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if XO is selling after one year at

(1)$98

(2) $90;

(3)$82

What is the relationship between your percentage return and the percentage change in the price of XO? Assume that XO pays no dividends.

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

Answer 1

You buy 300 shares selling at $90 per share.

Total cost = 90 * 300 = 27,000

Out of this, you pay 20,000 from your own money and borrow the remaining 7,000 [ 27,000 - 20,000]

A. So, if the equity increases to $98/share, you made: 98 * 300 - 27,000 = 2,400

Percentage gain = 2,400 / 20,000 = 0.12 = 12%

B. If it remains constant at $90, then there will be no change. Hence, return = 0%

C. If equity decreases to $82, you made: 82 * 300 - 27,000 = -2,400

Percentage gain = -2,400 / 20,000 = -0.12 = - 12%