Question

Suppose that Xtel is currently selling at $50/share. You buy 700 shares using $28,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 7%.

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
B If the maintenance margin is 20%, how low can Xtel's price fall before you get a margin call?
C. How would your answer to requiremwnt 2 change if you had finances the initial purchase with only $17,500 of your own money? (strike price)
D. What is the rate of return on your margined position (assuming you invest $28,000 of yur own money) if Xtel is selling after one year at (a) $56 (b) $50 (c) $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

Answer:

Explanation:

A. total value of purchase = 700*35 = 35,000

broker loan = 35,000-28,000 = 7,000

your contribution = 28,000

interest = 7% * 7000 = 490

a) % increase = (56-50)*700/28000 = 15%

b) % increase = 0%; price is same

c)% increase = (44-50)*700/28,000 = -15.00%

B.

80% = 7,000

20% = 7,000*20/80 = 1,750

reduction in value = 28,000 - 1,750 = 26,250

reduction in price per share = 26,250/700 = 37.5

price for margin call = 50 - 37.5 = 12.5

C broker contribution = 10,500

80% = 10,500

20% = 10,500*20/80 = 2,625

loss allowed per share = (17,500 - 2,625)/700 = 20.54

price for margin call = 50 - 20.54 = 29.46

Answer 2

Answer:

Explanation: The total cost of the purchase is: $50 X 700 = $35,000.

$7,000 is borrowed from the broker.

A. (a) Percentage increase when price changes to ($56 x 700) - $7,000 = $39,200 - $7,000 = $32,200

Percentage gain = ($32,200 - $28,000)/$28,000 = $4,200/$28,000 = 0.15 = 15%.

(b) Percentage increase when the price remains the same = 0.

(c) Percentage increase when the price falls to ($44 x 700) - $7,000 = $30,800 - $7,000 = $23,800.

Percentage gain = ($23,800 - $28,000)/$28,000 = -$4,200/$28,000 = -0.15 =-15%.

B. The value of 700 shares is 700P, where P is price. Equity is (700P - $7,000). Margin call will be received when:

(700P - $7,000)/700P = 0.80 = 80%

20% = (7,000 x 20)/80 = $1,750

Reduction in value = $28,000 - $1,750

$26,250

Reduction in price per share:

$26,250/700 = $37.5

Margin call = $50 - $37.5 = $12.5 or lower.

C. Contribution of broker = $10,500

80% = $10,500

20% = ($10,500 x 20)/80 = $2,625

Loss allowed per share = ($17,500 - $2,625)/700 = $20.54

Margin call = 50 - 20.54 = $29.46 or lower.

D. Since the margin loan is 7%, by the end of the year the amount owed to the broker grows to:

$7,000 x 1.07 = $7,490

(i) Rate of return after one year at $56

(700 x 56) - 7,490 - 28,000/28,000 = 3,710/28,000 = 0.1325 = 13.25%.

(ii) Rate of return after one year at $50

(700 x 50) - 7,490 - 28,000/28,000 = -490/28,000 = -0.0175 = -1.75%.

(iii) Rate of return after one year at $44

(700 x 44) - 7,490 - 28,000/28,000 = -4,690/28,000 = -0.1675 = -16.75%.

E. 80% = $7,300

20% = $7,300 x 20/80 = $1,825

Reduction in value = $28,000 - $1,825 = $26,175

Reduction in price per share = $26,175/700 = $37.39

Margin call = $50 - $37.39 = $12.61 or lower.