Question

Suppose that you sell short 200 shares of Xtel, currently selling for $50 per share, and give your broker $6,000 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) $56; (ii) $50; (iii) $45? Assume that Xtel pays no dividends.

b. If the maintenance margin is 25%, how high can Xtel’s price rise before you get a margin call?

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.

Answer 1

Part a)

The rate of return on short position can be calculated with the use of following formula:

Rate of Return = (-Number of Shares*Change in Price)/Invested Amount*100

_____

(i)

Rate of Return After One Year if Stock is Selling at $56

Rate of Return = (-200*(56 - 50))/6,000*100 = -20%

____

(ii)

Rate of Return After One Year if Stock is Selling at $50

Rate of Return = (-200*(50 - 50))/6,000*100 = 0%

____

(iii)

Rate of Return After One Year if Stock is Selling at $45

Rate of Return = (-200*(45 - 50))/6,000*100 = 16.67%

_____

Part b)

The price at which you will get a margin call can be calculated with the use of equation given below:

Maintenance Margin = (Total Assets in Margin Account - Total Liabilities)/(Number of Shares*Price At Which You Will get Margin Call)

where, Maintenance Margin = 25%, Total Assets in Margin Account = 200*50 (from sale of stock) + 6,000 (initial margin) = $16,000 and Total Liabilities = 200P (where P = Price At Which You Will get Margin Call)

Substituting values in the above formula, we get,

25% = (16,000 - 200P)/200P

Rearranging Values, we get,

200P*25% = 16,000 - 200P

200P + 50P = 16,000

Solving for P, we get,

P = 16,000/250 = $64

Therefore, you will get a margin call if the price is $64 or higher. As soon as the price reaches $64, you will get a margin call.

_____

Part c)

Recalculation of Part a) with dividends

The rate of return on short position can be calculated with the use of following formula:

Rate of Return = (-Number of Shares*Change in Price - Dividend)/Invested Amount*100

_____

(i)

Rate of Return After One Year if Stock is Selling at $56

Rate of Return = (-200*(56 - 50) - (200*1))/6,000*100 = -23.33%

____

(ii)

Rate of Return After One Year if Stock is Selling at $50

Rate of Return = (-200*(50 - 50) - (200*1))/6,000*100 = -3.33%

____

(iii)

Rate of Return After One Year if Stock is Selling at $45

Rate of Return = (-200*(45 - 50) - (200*1))/6,000*100 = 13.33%

_____

Recalculation of Part b) with dividends

The price at which you will get a margin call can be calculated with the use of equation given below:

Maintenance Margin = (Total Assets in Margin Account - Total Liabilities)/(Number of Shares*Price At Which You Will get Margin Call)

where, Maintenance Margin = 25%, Total Assets in Margin Account = 200*50 (from sale of stock) + 6,000 (initial margin) = $16,000 and Total Liabilities = (200P + Dividends) = (200P + 200) (where P = Price At Which You Will get Margin Call)

Substituting values in the above formula, we get,

25% = (16,000 - (200P + 200))/200P

Rearranging Values, we get,

50P = 15,800 - 200P

P = 15,800/250 = $63.20

Therefore, you will get a margin call if the price is $63.20 or higher. As soon as the price reaches $63.20, you will get a margin call.