Question

q 17 A stock was trading at $116.85 at the end of year 1. It was trading at the end of year 2 at $110.15 immediately after giving a dividend of $3.50. At the end of year 3. it was trading at $120.35 immediately after giving a dividend of $3.70. Finally, it was trading at $130.45 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?

Answer 1

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 = ($110.15 - $116.85) + $3.80 / $116.85

Return = (-$6.7 + $3.50) / $116.85

Return = -$3.2 / $116.85 = -2.74%

For year 3:

Return = ($120.35 - $110.15) + $3.7 / $110.15

Return = ($10.2 + $3.7) / $110.15

Return = $13.9 / $110.15 = 12.62%

For year 4:

Return = ($130.45 - $120.35) + $0 / $120.35

Return = ($10.1 + $0) / $120.35

Return = $10.1 / $120.35 = 8.39%

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 = (-2.74 + 12.62 + 8.39) / 3

Arithmetic average return = 18.27 / 3 = 6.09 %