Question

Suppose that you sell short 200 shares of Xtel, currently selling for $80 per share, and give your broker $10,000 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) $85; (ii) $80; (iii) $75? 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)

Assets = Invested Cash + Proceeds from Short Sale = $10,000 + ($80 *200) = $26,000

Liability = Value of 200 Shares Owed = 200P

Equity = Assets – Liabilities = $26,000 – 200P

i.Price to $85

Equity = Assets – Liabilities = $26,000 – ($85*200) = $26,000 – $17,000 = $9,000

Return = $9,000/$10,000 – 1 = -0.1 = -10%

ii.Price at $80

Equity = Assets – Liabilities = $26,000 – ($80*200) = $26,000 – $16,000 = $10,000

Return = $10,000/$10,000 – 1 = 0%

iii.Price at $75

Equity = Assets – Liabilities = $26,000 – ($75*200) = $26,000 – $15,000 = $11,000

Return = $11,000/$10,000 – 1 = 0.1 = 10%

B)

Assets = Invested Cash + Proceeds from Short Sale = $10,000 + ($80*200) = $26,000

Liability = Value of 200 Shares Owed = 200P

Equity = Assets – Liabilities = $26,000 – 200P

Margin Rate = Equity/Liabilities = ($26,000 – 200P)/200P

You will receive a margin call if Margin Rate < 0.25

Margin Call if ($26,000 – 200P)/200P < 0.25

P> $26000/(1.25*200)

P>$26000/250

P>$104

Margin call if P > $104.00

C) The dividend is either payable to the entity from which the short borrowed the shares – in which case the liability is greater by the dividend amount or the dividend has been paid to the entity from which the short borrowed the shares – in which case the assets (cash) is lower.

Assets = Invested Cash + Proceeds from Short Sale – Dividend = $10,000 + ($80*200) – ($1*200) = $25,800

Liability = Value of 200 Shares Owed = 200P

Equity = Assets – Liabilities = $25,800 – 200P

i.Price to $85

Equity = Assets – Liabilities = $25,800 – ($85*200) = $25,800 – $17,000 = $8800

Return = $8,800/$10,000 – 1 = -0.12 = -12%

ii.Price at $80

Equity = Assets – Liabilities = $25,800 – ($80*200) = $25,800 – $16,000 = $9,800

Return = $9,800/$10,000 – 1 = -0.02 = - 2%

iii.Price at $75

Equity = Assets – Liabilities = $25,800 – ($75*200) = $25,800 – $15,000 = $10,800

Return = $10,800/$10,000 – 1 = 0.08 = 8%