Question

Suppose that you sell short 500 shares of Xtel, currently selling for $70 per share, and give your broker $25,000 to establish your margin account.

A. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if Xtel stock is selling at: (i) $74; (ii) $70; (iii) $66? Assume that Xtel pays no dividends. (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.)

i	Rate of Return		%
ii	Rate of Return		%
iii	Rate of Return		%

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

Margin call will be made at price ______ or higher

c. Redo parts (a) and (b), but now assume that Xtel also has paid a year-end dividend of $1 per share. The prices in part (a) should be interpreted as ex-dividend, that is, prices after the dividend has been paid. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

i	Rate of Return		%
ii	Rate of Return		%
iii	Rate of Return		%

Margin call will be made at price _______ or higher

Answer 1

A.

Note:- Consider all amounts in $

If share price is 74; we need to purchase shares at 74 and sell at 70 therefore:-
Return Per share is	Short price - purchase price
=70-74	-4
Return for 500 shares(-4*500)	-2000
Investment in shares(500*70)	35000
Rate of return(-2000/35000)	-5.71%
If share price is 70; we need to purchase shares at 70 and sell at 70 therefore:-
Return Per share is	Short price - purchase price
=70-70	0
Return for 500 shares (500*0)	0
Investment in shares(500*70)	35000
Rate of return(0/35000)	0.00%
If share price is 66; we need to purchase shares at 66 and sell at 70 therefore:-
Return Per share is	Short price - purchase price
70-66	4
Return for 500 shares(500*4)	2000
Investment in shares(70*500)	35000
Rate of return(2000/35000)	5.71%

B.

Key take from the question is, we have already made a deposit of $25000 in the margin account

At the current of price $70 per share margin required @ 25% is

= $70*500*25%

=$8750

Now the broker can call for margin money only if $25000 is less than the 25% of the total actual shares price. Therefore let us say "Y" is total investment required for 500 shares at increased share price and "X" is the increased share price per share.

=>   Y*25% = 25000

=> Y = 100000

Therfore total value of shares is $100000 which is the highest value for the existing margin, any amount which is more than $100000 requires additional margin money

=> X*500 = 100000

=> X = 200

From the above it is clear that if the share price is more than $200 per share it requires additional margin money. Therefore margin cal will be made at share price of $ 201 or more. C. If share price is 74; we need to purchase shares at 74 and sell at 70 therefore:- Return Per share is Short price - purchase price + Dividend received -3 Return for 500 shares -1500 Investment in shares 35000 Rate of return -4.29% If share price is 70; we need to purchase shares at 70 and sell at 70 therefore:- Return Per share is Short price - purchase price + Dividend received 1 Return for 500 shares 500 Investment in shares 35000 Rate of return 1.43% If share price is 66; we need to purchase shares at 66 and sell at 70 therefore:- Return Per share is Short price - purchase price 5 Return for 500 shares 2500 Investment in shares 35000 Rate of return 7.14% If we assume that dividend is directly recevied to the bank account of investor the margin money call will be same as answer B.