Question

A stock was trading at $21.85 at the end of year 1. It was trading at the end of year 2 at $22.18 immediately after giving a dividend of $0.30. At the end of year 3. it was trading at $21.54 immediately after giving a dividend of $0.32. Finally, it was trading at $23.36 at the end of year 4 without giving out any dividend. What was the geometric average annual return of this stock for the three years between years 1 and 4?

Answer 1

A stock was trading at $21.85 at the end of year 1. It was trading at the end of year 2 at $22.18 immediately after giving a dividend of $0.30. At the end of year 3. it was trading at $21.54 immediately after giving a dividend of $0.32. Finally, it was trading at $23.36 at the end of year 4 without giving out any dividend. What was the geometric average annual return of this stock for the three years between years 1 and 4?

- Stock price at year end 1(P1) =$21.85

Stock price at year end 2(P2) =$22.18

Dividend paid during the time = $0.30

Return in year 2 = [(P2 - P1) + Dividend]/P1

=[($22.18 - $21.85) +$0.30]/$21.85

= 2.8833%

- Stock price at year end 2(P2) =$22.18

Stock price at year end 3(P3) =$21.54

Dividend paid during the time = $0.32

Return in year 3 = [(P3- P2) + Dividend]/P2

=[($21.54 - $22.18) +$0.32]/$22.18

= -1.4427%

- Stock price at year end 4(P4) =$23.36

Stock price at year end 3(P3) =$$21.54

Dividend paid during the time = $0

Return in year 2 = [(P4 - P3) + Dividend]/P3

=[($23.36 - $21.54) +$0]/$21.54

= 8.4494%

Calculating the Geometric average annual return of this stock for the three years between years 1 and 4:-

Geometric Average Annual Return

= 1.03218 - 1

= 3.22%

So, the Geometric Average Annual Return is 3.22%

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