Suppose you buy a round lot of DG Solutions stock on 60% margin when it is selling at $55 a share. The broker charges a 10 percent annual interest rate and commissions are 3 percent of the total stock value on both the purchase and the sale. If at year end you receive a $1.10 per share dividend and sell the stock for 55 5/8, what is your rate of return on the investment?
A)-10.38%
B)-12.84%
C)-10.95%
D)21.84%
E)28.38%

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the amount of money we borrowed to purchase the stock. As we purchased the stock on 60% margin, we put down 40% of the total value, which is:

40% x $55 x 100 = $2,200

So, we borrowed $3,300 to purchase the stock.

Next, we need to calculate the commission we paid on the purchase:

3% x ($55 x 100) = $165

Therefore, the total cost of our investment is:

$3,300 + $165 = $3,465

At the end of the year, we received a dividend of $1.10 per share. As we purchased a round lot of stock (which typically contains 100 shares), we received a total dividend of:

$1.10 x 100 = $110

Now, we need to calculate the proceeds from selling the stock. We sold at a price of 55 5/8, which is the same as 55.625 per share. As we purchased a round lot of stock, we sold 100 shares for a total of:

100 x $55.625 = $5,562.50

We also need to calculate the commission we paid on the sale:

3% x ($55.625 x 100) = $166.88

So, our net proceeds from selling the stock are:

$5,562.50 - $166.88 = $5,395.62

Finally, we can calculate our rate of return on the investment:

Total Gain = Proceeds - Cost - Interest - Commission - Dividend 
Total Gain = $5,395.62 - $3,465 - ($3,300 x 10%) - $165 - $110 
Total Gain = $919.62

Rate of Return = (Total Gain / Cost) x 100% 
Rate of Return = ($919.62 / $3,465) x 100% 
Rate of Return = 26.51%

Therefore, our rate of return on the investment is 26.51%. The closest answer choice is C.

Suppose You Buy a Round Lot of DG Solutions Stock