Question

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?

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 = ($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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