Question

Suppose that XTel currently is selling at $50 per share. You buy 600 shares using $22,500 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 (a) $55; (b) $50; (c) $45? (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.)

Percentage Gain?

Percentage Gain?

Percentage Gain?

b. If the maintenance margin is 25%, how low can XTel’s price fall before you get a margin call? (Round your answer to 2 decimal places.)

Price?

c. How would your answer to requirement 2 would change if you had financed the initial purchase with only $15,000 of your own money? (Round your answer to 2 decimal places.)

Strike Price ?

d. What is the rate of return on your margined position (assuming again that you invest $22,500 of your own money) if XTel is selling after one year at (a) $55; (b) $50; (c) $45? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Rate Of Return?

Rate Of Return?

Rate Of Return?

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.)

Price ?

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Answer 1

a). Total worth of shares = share price*number of shares bought = 50*600 = 30,000

Loan taken = 30,000 - amount invested = 30,000 - 22,500 = 7,500

Net worth of the account if share price is 55 = (55*600) - 7,500 = 33,000 - 7,500 = 25,500

%age gain = (net worth/amount invested) -1 = (25,500/22,500) -1 = 13.33%

If share price is constant at 50 then there is no gain or loss so %age gain = 0

If share price is 45, then net worth of the account = (45*600) - 7,500 = 27,000 - 7,500 = 19,500

%age gain = (19,500/22,500)-1 = -13.33%

b). Margin rate = (Assets - Liabilities)/Assets

Asset = 600p where p = share price

Liability = loan = 7,500

25% = (600p - 7,500)/600p

150p = 600p - 7,500

-450p = -7,500

p = 16.67

So, if the price falls below 16.67, there will be a margin call.

c). Initial market value = 50*600 = 30,000

Loan = 30,000 - 15,000 = 15,000

Then if share price is p,

25% = (600p - 15,000)/600p

450p = 15,000

p = 33.33 (Margin call would happen if the price fell below this in the case of loan being 15,000)

d). Total loan due after 1 year = loan*(1+i) = 7,500*(1+8%) = 8,100

Net worth if share price is $55 = (55*600) - 8,100 = 33,000 - 8,100 = 24,900

Net worth if share price is $50 = (50*600) - 8,100 = 30,000 - 8,100 = 21,900

Net worth if share price is $45 = (45*600) - 8,100 = 27,000 - 8,100 = 18,900

%age gain (share price $55) = (24,900/22,500) -1 = 10.67%

%age gain (share price $50) = (21,900/22,500) -1 = -2.67%

%age gain (share price $45) = (18,900/22,500) -1 = -16.00%

e). Margin rate = (Asset - Loan)/Asset

Asset = 600p where p = share price

After one year, loan amount = 8,100 (calculated in part d)

25% = (600p - 8,100)/600p

450p = 8,100

p = 18.00 (Margin call will happen if the price falls below this)