Suppose you purchase one share of the stock of Volatile Engineering Corporation at the beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend and buy one more share for $30. At the end of year 2, you receive total dividends of $4 (i. e., $2 for each share) and sell the shares for $36.45 each. The dollar-weighted return on your investment is:

8.53%

Explanation:

The return on investment can be calculated by using the following formula:

ROI = Net Profit / Investment     * 100%

For Year 1,

Net profit is -$4 (Step1)

Investment is the opening value of the stock which is $36 per share

So by putting values, we have:

ROI =  -$4 / $36    * 100%   = -11.11%

For Year 2,

Net profit is $4.45 (Step1)

Investment is the opening value of the stock which is $30 per share

So by putting values, we have:

ROI =  $4.45 / $30    * 100%   = 28.17%

Dollar-Weighted Return on your Investment

Dollar-Weighted ROI = (28.17% + (11.11%)) / 2 = 8.53%

Step 1. Net Profit

Net profit for the Y1 = Dividend Paid + Loss on investment due to decrease in value of share

The Dividend Paid here is $2

The Loss on investment due to decrease in value of share is the difference of the initial share value and the price of the share at the end of the year which is Minus $6 ($30 Shares closing value - $36 shares opening value).

So by putting values, we have:

Net profit for the Y1 = $2 + (-$6) = -$4

Similarly,

Net profit for the Y2 = $4 Dividend + $36.45 Shares closing value - $36 shares opening value = $4.45

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30