Question

Suppose that you sell short 500 shares of Intel, 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 1 year if Intel stock is selling at: (i) $74; (ii) $70; (iii) $66? Assume that Intel pays no dividends.

  

(i) Rate of return	%
(ii) Rate of return	%
(iii) Rate of return	%

b.

If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin call? c. Redo parts (a) and (b), but now assume that Intel 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.         (i) Rate of return %   (ii) Rate of return %   (iii) Rate of return %      Margin call will be made at price $ or higher

Answer 1

a)

Assets = Invested Cash + Proceeds from Short Sale

= 25000 + 500 * 70

= 60000

Liability is the Value of 500 Shares Owed

= 500 * P

Equity = Assets – Liabilities

= 60000 - 500P

i) At price 74

Equity = Assets – Liabilities

= 60000 - 500 * 74 = 23000

Return = Equity / Invested Cash = ( 23000 / 25000 ) - 1

= - 0.08 = - 13%

ii) At price 70

Equity = Assets – Liabilities

= 60000 - 500 * 70 = 25000

Return = Equity / Invested Cash = ( 25000 / 25000 ) - 1 = 0%

ii) At price 66

Equity = Assets – Liabilities

= 60000 - 500 * 66 = 27000

Return = Equity / Invested Cash = ( 27000 / 25000 ) - 1 = 8 %

b)

Assets = Invested Cash + Proceeds from Short Sale

= 25000 + 500 * 70

= 60000

Liability is the Value of 500 Shares Owed

= 500 * P

Equity = Assets – Liabilities

= 60000 - 500P

Margin Rate = Equity / Liabilities = (60000 - 500P) / 500 * P

You will receive a margin call if Margin Rate < 0.25

[(60000 - 500P) / 500 * P] < 0.25

Evaluate for P

You will receive margin call if price P is > 96