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Suppose you purchase one share of the stock of Red Devil Corporation at the beginning of year 1 for $44.75. At the end of year 1, you receive a dividend of $2 and buy one more share for $48.75. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each share), and sell the shares for $56.75 each. What is the time-weighted return on your investment? (Round your answer to 2 decimal places. Do not round intermediate calculations.)

Answer :

Solution :

Year : 0

Price : $ 44.75

Year : 1

Price : $48.75

Dividend : 2

Return : [tex]$\frac{48.75+2-44.75}{44.75}$[/tex]

             = 13.41 %

Year :2

Price : $ 56.75

Dividend : 2

Return : [tex]$\frac{56.75+2-48.75}{48.75}$[/tex]

           = 20.51%

The time weighted return = [tex]$\left((1+r_1)\times (1+r_2)\right)^{1/2}-1$[/tex]

                                           = [tex]$\left((1+0.1341)\times (1+0.2051)\right)^{1/2}-1 $[/tex]

                                           = 16.91%

It is also called the geometric return.

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