Question

# A stock was trading at \$123.45 at the end of year 1. It was trading at...

A stock was trading at \$123.45 at the end of year 1. It was trading at the end of year 2 at \$116.75 immediately after giving a dividend of \$4.70. At the end of year 3. it was trading at \$126.95 immediately after giving a dividend of \$4.90. Finally, it was trading at \$137.05 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 = (\$116.75 - \$123.45) + \$4.7 / \$123.45

Return = (-\$6.7 + \$4.7) / \$123.45

Return = -\$2 / \$123.45 = -1.62%

For year 3:

Return = (\$126.95 - \$116.75) + \$4.90 / \$116.75

Return = (\$10.2 + \$4.90) / \$116.75

Return = \$15.1 / \$116.75 = 12.93%

For year 4:

Return = (\$137.05 - \$126.95) + \$0 / \$126.95

Return = (\$10.1 + \$0) / \$126.95

Return = \$10.1 / \$126.95 = 7.96%

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 = (-1.62 + 12.93 + 7.96) / 3

Arithmetic average return = 19.27 / 3 = 6.42 %

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