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, what will be your rate of return after one year if XTel stock is selling at (i) $44, (ii) $40, (iii) $36? 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

The rate of return on a short sale varies depending on the stock's final price. Without dividends, returns are -13.33% at $44, 0% at $40, and +13.33% at $36, based on the initial margin of $15,000. The stock's price can rise to $120 before a margin call, and a dividend would slightly impact these figures.

Step-by-step explanation:

The calculation of the rate of return on a short sale involves determining the profit or loss from the sale of the stock at different price levels and comparing it to the initial value of the margin account.

Part A without Dividend

• (i) At $44 per share, you would need to buy back the 500 shares for $22,000. Since you originally sold them for $20,000, your loss would be $2,000. With no interest on your margin balance, your rate of return would be -13.33% (loss of $2,000 / $15,000 initial margin).
• (ii) At $40 per share, there is no profit or loss since the buyback price equals the initial sale price, leading to a 0% return.
• (iii) At $36 per share, the buyback costs you $18,000, giving you a profit of $2,000 and a rate of return of +13.33% (profit of $2,000 / $15,000 initial margin).

Part B without Dividend

To avoid a margin call, the price per share cannot rise to the point where your equity falls below 25% of the total value of the 500 shares. The calculation for the threshold price before a margin call is triggered is as follows: $15,000 / (0.25*500) = $120 per share. Therefore, XTel's price can rise up to $120 before a margin call.

With Dividend

When accounting for a dividend of $1 per share, your calculations for parts A and B must account for the additional cost of the dividend payment, which totals $500 (500 shares * $1 per share). This will slightly alter the rate of return figures and the price threshold for a margin call.