Suppose that you sell short 500 shares of XTel, currently selling for $40 per sh

Question

Suppose that you sell short 500 shares of XTel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account. a. If you earn no interest on the funds in your margin account, Assume that XTel pays no dividends. So what will be your rate of return after one year if XTel stock is selling at: (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) (i) $44 Rate of return 13.33 % (ii) $40 Rate of return 00% (ii) $36 Rate of return 13.33 0 % b. If the maintenance margin is 25%, how high can XTel's price rise before you get a margin call? S 35,000 * 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 value should be indicated by a minus sign. Round your answers to 2 decimal places.) (i) $44 Rate of return 16,67 % (ii) $40 Rate of return 3.33 % (ii) $36 Rate of return 10.00 % $ 55.20 O

Explanation / Answer

b. Assets = Invested Cash + Proceeds from Short Sale = $15,000 + ($40 x 500) = $35,000

Liability = Value of 500 Shares Owed = 500P

Equity = Assets – Liabilities = $35,000 – 500P

Margin Rate = Equity/Liabilities = ($35,000 – 500P)/500P

0.25 x 500P = $35,000 - 500P

Or, P = $35,000/625 = $56

c. Assets = Invested Cash + Proceeds from Short Sale – Dividend

= $15,000 + ($40 x500) – ($1 x500) = $34,500

Liability = Value of 500 Shares Owed = 500P

Equity = Assets – Liabilities = $34,500 – 500P

1.Price at $44

Equity = Assets – Liabilities = $34,000 – ($44 x5,000) = $34,500 – $22,000 = $12,500

Return = $12,000/$15,000 – 1 = -0.1667 = -16.67%

2.Price at $40

Equity = Assets – Liabilities = $34,500 – ($40 x 500) = $34,500 – $20,000 = $14,500

Return = $14,400/$15,000 – 1 = -4%

3.Price at $36

Equity = Assets – Liabilities = $34,500 – ($36 x 500) = $34,500 – $18,000 = $16,500

Return = $16,500/$15,000 – 1 = 10%

Now,

Assets = Invested Cash + Proceeds from Short Sale - Dividend

= $15,000 + ($40 x 500) - $1 x 500 = $34,500

Liability = Value of 500 Shares Owed = 500P

Equity = Assets – Liabilities = $34,500 – 500P

Margin Rate = Equity/Liabilities = ($34,500 – 500P)/500P

0.25 x 500P = $34,500 - 500P

Or, P = $34,500/625 = $55.2

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