A stock has had the following year-end prices and dividends: Year Price Dividend1 $43.55 - 2 48.53 $.87 3 57.45.90 4 45.53.95 5 52.45 1.00 6 61.53 1.08 What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.)

10.27% and 9.11%

Explanation:

The computation is shown below:

Given that

Year Price Dividend Return

1 $43.55

2 $48.53 $.87 13.43%

3 $57.45 $.90 20.23%

4 $45.53 $.95 - 19.90%

5 $52.45 $1.00 17.39%

6 $61.53 $1.08 19.37%

Total 51.34%

Now the arithmetic average return is

= 51.34% : 5

= 10.27%

And, the geometric average return is

= ((1 + 13.4328%) * (1 + 20.2349%) * (1 - 19.9049%) * (1 + 17.3951%) * (1 + 19.3708%)) ^ (1 : 5) - 1

= 9.11%

Working Note:

Rate of Return from year 1-2 = (Ending Price - Beginning Price+Dividend) : Beginning Price

= ($48.53 - $43.55 + 0.87) : $43.55

= 13.4328%

Rate of Return from 2-3 = ($57.45 - $48.53 + $0.90) : $48.53

= 20.2349%

Rate of Return from 3-4 = ($45.53 - $57.45 + $0.95) : $57.45

= - 19.9049%

Rate of Return from 4-5 = ($52.45 - $45.53 + 1) : $45.53

= 17.3951%

Rate of Return from 5-6 = ($61.53 - $52.45 + $1.08) : $52.45

= 19.3708%