Question

# A stock was trading at \$125.10 at the end of year one. It was trading at...

A stock was trading at \$125.10 at the end of year one. It was trading at the end of year two at \$118.40 immediately after giving a dividend of \$5.00. At the end of year three. it was trading at \$128.60 immediately after giving a dividend of \$5.20. Finally, it was trading at \$138.70 at the end of year 4 without giving out any dividend. What was the arithmetic average annual return of this stock for the three years between years 1 and 4?

First we will calculate the return for each year by the following formula:

Return = (End of period stock price - Beginning period stock price) + Dividend / Beginning period stock price

For year 2:

Return = (\$118.4 - \$125.10) + \$5 / \$125.10

Return = (-\$6.7 + \$5) / \$125.10

Return = -\$1.7 / \$125.10 = -1.36%

For year 3:

Return = (\$128.6 - \$118.4) + \$5.2 / \$118.4

Return = (\$10.2 + \$5.2) / \$118.4

Return = \$15.4 / \$118.4 = 13%

For year 4:

Return = (\$138.7 - \$128.6) + \$0 / \$128.6

Return = (\$10.1 + \$0) / \$128.6

Return = \$10.1 / \$128.6 = 7.85%

Now, we will calculate the arithmetic average return as per below:

Arithmetic average return = Sum of returns / Number of returns

Putting the values in the above formula, we get,

Arithmetic average return = (-1.36 + 13 + 7.85) / 3

Arithmetic average return = 19.49 / 3 = 6.50 %

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