Series 7 Exam Question 60: Answer and Explanation

Question: 60

Ayla K. is employing a dollar cost averaging program for purchasing shares of Decco aggressive growth fund. She has been purchasing $440 per month of the fund for the past 4 months. The first month, she purchased the fund at $20.00 per share; the second month, $22.00 per share; the third month, $22.00 per share; the fourth month $20.00 per share. What is Ayla's average cost per share?

• A. $20.00
• B. $20.95
• C. $21.00
• D. $21.07

Correct Answer: B

Explanation:

B. Dollar cost averaging brings the average dollar price per share down when the fund is fluctuating in value. Dollar cost averaging, which is investing the same dollar amount periodically, allows the investor to purchase more shares when the price is low and less when the price is high. Now, you might think that since Ayla purchased shares at $22 and $20, that she paid an average of $21 per share. However, since she was able to purchase more shares when the price was lower, her average cost per share is less than $21. She was able to purchase 22 shares per month when the price was low and 20 shares per month when the price was higher.

$1\text{st}\text{and}\text{4th}\text{months}=\frac{\text{\$440}\text{invested}}{\text{\$20}\text{per}\text{share}}=22\text{shares}\text{per}\text{month}$

$\text{2nd}\text{and}\text{3rd}\text{months}=\frac{\text{\$440}\text{invested}}{\text{\$22}\text{per}\text{share}}=20\text{shares}\text{per}\text{month}$

Over the four months, Ayla invested a total of $1,760 ($440 × 4) and purchased a total of 84 shares (22 + 20 + 20 + 22). The average cost per share is $20.95:

$\text{average}\text{cost}\text{per}\text{share}=\frac{\text{total}\text{amount}\text{invested}}{\text{no}\text{.}\text{of}\text{shares}\text{purchased}}=\frac{\$1,760}{\text{84}\text{shares}}=\$20.95$