Question

Suppose that XTel currently is selling at $50 per share. You buy 900 shares using $36,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 9%.

a. What is the percentage increase in the net worth of your brokerage account if the price of XTel immediately changes to (a) $56; (b) $50; (c) $44? (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. If the maintenance margin is 20%, how low can XTel’s price fall before you get a margin call? (Round your answer to 2 decimal places.)

c. How would your answer to requirement 2 would change if you had financed the initial purchase with only $22,500 of your own money? (Round your answer to 2 decimal places.)

d. What is the rate of return on your margined position (assuming again that you invest $36,000 of your own money) if XTel is selling after one year at (a) $56; (b) $50; (c) $44? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
e. Continue to assume that a year has passed. How low can XTel’s price fall before you get a margin call? (Round your answer to 2 decimal places.)

Answer 1

Total Purchase cost : $ 50 X 900 = $ 45000.

You borrow $ 9000 ($ 45000 - $ 36000) from your  broker, and invest $ 36000 of your own funds. Your margin account starts out with equity of $ 36000.

a. (i) Equity increases to: ($ 56 X 900) - $ 9000 = $ 41400

       Percentage gain = $ 5400/ $36000 = 15%

    (ii) With price unchanged that is $ 50, equity remains unchanged.

         Percentage gain = 0

    (iii) Equity falls to : ($ 44 X 900) - $ 9000 = $ 30600

         Percentage gain = - $5400/ $36000 = - 15%

b. The value of the 900 shares is 900P. Equity is (900P – $ 9000). You will receive margin call when:

   (900P – $ 9000) / 900P = 0.20 , Therefore P = $ 12.5 or lower

c. The value of the 900 shares is 900P. But now we have borrowed $22,500 instead of $9,000. Therefore, equity is (500P –  

    $22,500). You will receive a margin call when:

(900P – $ 22,500) / 900P = 0.20 , Therefore P = $ 31.25 or lower.

    With less equity in the account, you are far more vulnerable to a margin call.

d. By the end of the year, the amount of the loan owed to the broker grows to:$9,000 X 1.09 =$ 9810

    The equity in our account is (900P – $9,810). Initial equity was $ 36,000. Therefore, your rate of return after one year is      

    as follows :

    (i) [($ 900 X 56 - $9810 - $ 36,000] / $36,000 = 12.75%

(II) [($ 900 X 50 - $9810 - $ 36,000] / $36,000 = - 2.25%

   (III) [($ 900 X 44 - $9810 - $ 36,000] / $36,000 = - 17.25%

e. The value of the 900 shares is 900P. Equity is (900P – $9,810). We will receive a margin call when

   (900P – $9,810) / 900P = 0.20 . Therefore P = 13.63% or lower.