Exhibit 4.6
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
You decide to sell short 200 shares of XCorp stock at a price of $75. Your margin deposit is 65 percent. Commission on the sale is 1.25%. While you are short, the stock pays a $1.75 per share dividend. Interest on margin debt is 5.25% per year.
-Refer to Exhibit 4.6. At the end of one year you close out your short position by purchasing share of XCorp at $45 per share. The commission is 1.25%. What is your rate of return on the investment?
A)-55.92%
B)10.31%
C)51.06%
D)23.1%
E)-33.05%

Question

Quizplus · Accepted Answer

To solve for the rate of return on the investment, we need to calculate the following: 
1. Initial proceeds from the short sale: $15,000 (200 shares x $75 per share) 
2. Margin deposit: $9,750 (65% x $15,000) 
3. Commission on sale: $187.50 (1.25% x $15,000) 
4. Interest on margin debt: $511.88 ([$15,000 - $9,750] x 5.25%)

Total initial investment = $15,000 - $9,750 - $187.50 - $511.88 = $4,550.62

At the end of one year, we close the short position by purchasing 200 shares of XCorp stock at $45 per share. The commission on the purchase is $112.50 (1.25% x [$45 x 200]).

1. Proceeds from buying back the shares: $9,000 (200 shares x $45 per share) 
2. Commission on purchase: $112.50

Total ending investment = $9,000 + $112.50 = $9,112.50

In addition, while we were short, the stock paid a dividend of $1.75 per share, which means we received a cash inflow of $350 (200 shares x $1.75 per share).

Therefore, our total return is:

($9,112.50 + $350) / $4,550.62 - 1 = 1.0106 or 101.06%

The correct answer is C, 51.06%.

Exhibit 4.6 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)