Suppose you purchase 300 shares of stock at $75 per share with an initial Cash i

Question

Suppose you purchase 300 shares of stock at $75 per share with an initial Cash investment of $10000. If your broker requires 25% maintenance margin, at what share price will you be subject to a margin call? Suppose that the call money rate is 4% and you are charged 2% premium over this rate. Calculate your return on investment for each of the following share prices one year later. What would your rate of return be in each case if you purchased $10000 of stock with no margin? Assume that there are no dividends.

Explanation / Answer

Initial margin=10000

Maintenance Margin=25% of Initial Margin=.25*10000=2500

Let x be the share price at which margin call occurs,

Thus total margin position after this=Initial margin+Loss on share=10000-(75-x)*300

Total Margin at margin call=Maintenance Margin

=>10000-(75-x)*300=2500

=>7500=(75-x)*300 =>75-x=7500/300=25 =>x=75-25=50

Thus share price at which margin call occurs is $50.

a)at 85$,

total stock investment=75*300=22500,Initial cash investment=10000

rest 22500-10000=12500 is charged at 6% for 1 year,

profit from stock investment=300*(85-75)=3000

Interest on borrowing=12500*6%=750

Total profit made =profit from stock investment-Interest on borrowing=3000-750=2250

Return on investment=(2250/1000)-1=125%

b)

at 65$,

total stock investment=75*300=22500,Initial cash investment=10000

rest 22500-10000=12500 is charged at 6% for 1 year,

profit from stock investment=300*(65-75)=-3000

Interest on borrowing=12500*6%=750

Total profit made =profit from stock investment-Interest on borrowing=-3000-750=-3750

Return on investment=(-3750/1000)-1=-475%

a) with no margin,at 85$

%Return=(85/75)-1=13.33%

b)

with no margin,at 65$

%Return=(65/75)-1=-13.33%

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