Question

Suppose that you sell short 1000 shares of Xtel, currently selling for $60 per share, and give your broker $45,000 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) $66; (ii) $60; (iii) $54? 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.) Rate of return Rate of return 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 decima 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 $2 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.) Rate of return Rate of return Rate of return iii. Margin call will be made at price or higher

Answer 1

Currently 1,000 shares are short sold at a price of $60 per share. The margin account is of $45,000 thus, it means that $45,000 is paid by the investor himself (initial margin) and the remaining amount is borrowed. a. When there is no interest on the funds The rate of return after 1 year can be calculated using the following formula: (No. of shares short soldx change in price ) Rate of return= Margin account amount (1) If the stock is selling at $66 Calculate the rate of return as follows: No. of shares short sold xchange in price) Rate of retum = Margin account amount (1,000x ($60 - $66) $45,000 (1,000x(-$6) $45,000 -$6,000 $45,000 =-0.133333 or-13.3333% Therefore, the rate of return at price $66 is -13.3333%). (ii) If the stock is selling at $60 Calculate the rate of return as follows:

Rate of retum= _(No. of shares short soldxchange in price) Margin account amount (1,000x ($60 – $60)) $45,000 _(1,000x0) $45,000 $0 $45,000 =0% Therefore, the rate of return at price of $60 is 0%. (111) If the stock is selling at $54 Calculate the rate of return as follows: (No. of shares short sold xchange in price ) Rate of retum = Margin account amount (1,000x ($60 - $54) $45,000 (1,000 $6 $45,000 $6,000 $45,000 =0.133333 or 13.3333% Therefore, the rate of return at price of $54 is 13.3333%). The maintenance margin is given as 25%. To determine the price firstly calculate the total assets value in the margin account as follows:

Total assets in the margin account = Sale of the stock +Initial margin =(Number of shares short soldx Current price) + Initial margin =(1,000 shares $60)+$45,000 = $60,000+ $45,000 =$105,000 Thus, the value of total assets in the margin account is $105,000. Now, let the price be P at which margin call will be received by the broker. Calculate the price P as follows: $105,000 -(1,000 shares XP) _ (1,000 shares x P) $105,000-1,000XP = 0.25 x1,000x P $105, 000 - 1,000XP = 250XP (1,000xP)+(250XP) = $105,000 1,250% P = $105,000 $105,000 P = 1,250 = $84 or higher Thus, if the price reaches $84 or higher the investor will receive a margin call. c. When dividend of $2 per share is also paid Part (a) redone Calculate the amount of dividend paid on the total shares as follows: Dividend paid=Dividend per sharex Number of shares = $2 per share x1,000 shares = $2,000 Thus, the dividend repaid is $2,000.

Now, the rate of return can be calculated using the following formula: (No. of shares short sold x change in price )- Dividend repaid Rate of return= Margin account amount (i) If the stock is selling at $66 Calculate the rate of return as follows: (No. of shares short sold x change in price ) - Dividend repaid Rate of retum =( Margin account amount (1,000x ($60 – $66)) – $2,000 $45,000 (1,000x(-$6) -$2,000 $45,000 -$6,000-$2,000 $45,000 -$8,000 $45.000 =-0.177777 or -17.7778% Therefore, the rate of return at price $66 is -17.78%. (ii) If the stock is selling at $60 Calculate the rate of return as follows:

(No. of shares short sold x change in price ) - Dividend repaid Rate of retum = Margin account amount (1,000x ($60 - $60))-$2,000 $45,000 (1,000x0)-$2,000 $45,000 $0-$2,000 $45,000 -$2,000 $45.000 =-0.044444or-4.4444% Therefore, the rate of return at price of $60 is -4.44% (iii) If the stock is selling at $54 Calculate the rate of return as follows: (No. of shares short sold x change in price ) - Dividend repaid Rate of retum= Margin account amount (1,000x ($60-$54) - $2,000 $45,000 (1,000 $6) -$2,000 $45,000 $6,000-$2,000 $45,000 $4,000 $45,000 =0.088888 or 8.8888% Therefore, the rate of return at price of $54 is 8.89%.

Part (b) redone The amount of totals asset in the margin account will remain the same at $105,000. However, the amount of liabilities in the margin account will change. It will be the sum of the shares value (1,000 shares multiplied with the price P) and the dividend amount. Thus, the liabilities in the margin account is 1,000 P + $2,000 Now determine the price at which margin call will be received by the broker as follows: $105,000-(1,000 shares XP) - $2,000 -= 0.25 (1,000 sharesx P) $105,000-1,000ⓇP-$2,000 = 0.25x1,000 P $103,000-1,000 XP = 250XP (1,000ⓇP)+(250ⓇP) = $103,000 1,250x P = $103,000 $103,000 1, 250 = $82.4 or higher P = Thus, if the price reaches $82.4 or higher the investor will receive a margin call.