# IGM Realty had a price of $30,$30, $35,$33, and $25 at the end of the last five quarters. If... ## Question: IGM Realty had a price of$30, $30,$35, $33, and$25 at the end of the last five quarters. If IGM pays a dividend of $2 at the end of each quarter, what is the annual realized return on IGM? a. 8.61% b. 7.6% c. 7.10% d. 8.09% ## Annualized Return: Annualized return is the equivalent annual return from the investment or deposit. Annualized return is useful in comparing the feasibility and profitability of two or more investment opportunities. ## Answer and Explanation: The ending price of last 5 quarters and dividend in each quarter: Year Ending price Dividend Q1$30 $2 Q2$30 $2 Q3$35 $2 Q4$33 $2 Q5$25 $2 Quarterly returns are computed as follows: {eq}Return \ \left ( Q_2 \right ) \ = \ \dfrac{Ending \ price_{Q_2} \ - \ Beginning \ price_{Q_1} \ + \ Dividend_{Q_2}}{Beginning \ price_{Q_1}} \\ Return \ \left ( Q_2 \right ) \ = \ \dfrac{\$30 \ - \ \$30 \ + \ \$2}{\$30} \\ Return \ \left ( Q_2 \right ) \ = \ \dfrac{\$2}{\$30} \\ Return \ \left ( Q_2 \right ) \ = \ 0.0667 \\ Return \ \left ( Q_3 \right ) \ = \ \dfrac{Ending \ price_{Q_3} \ - \ Beginning \ price_{Q_2} \ + \ Dividend_{Q_3}}{Beginning \ price_{Q_2}} \\ Return \ \left ( Q_3 \right ) \ = \ \dfrac{\$35 \ - \ \$30 \ + \ \$2}{\$30} \\ Return \ \left ( Q_3 \right ) \ = \ \dfrac{\$7}{\$30} \\ Return \ \left ( Q_3 \right ) \ = \ 0.2333 \\ Return \ \left ( Q_4 \right ) \ = \ \dfrac{Ending \ price_{Q_4} \ - \ Beginning \ price_{Q_3} \ + \ Dividend_{Q_4}}{Beginning \ price_{Q_3}} \\ Return \ \left ( Q_4 \right ) \ = \ \dfrac{\$33 \ - \ \$35 \ + \ \$2}{\$35} \\ Return \ \left ( Q_4 \right ) \ = \ \dfrac{\$0}{\$35} \\ Return \ \left ( Q_4 \right ) \ = \ 0 \\ Return \ \left ( Q_5 \right ) \ = \ \dfrac{Ending \ price_{Q_5} \ - \ Beginning \ price_{Q_4} \ + \ Dividend_{Q_5}}{Beginning \ price_{Q_4}} \\ Return \ \left ( Q_5 \right ) \ = \ \dfrac{\$25 \ - \ \$33 \ + \ \$2}{\$33} \\ Return \ \left ( Q_5 \right ) \ = \ \dfrac{-\$6}{\\$33} \\ Return \ \left ( Q_4 \right ) \ = \ -0.1818 {/eq}

As there are returns for 4 quarters which constitutes a total year. The exacerbating duplication according to desires hypothesis will the yearly acknowledged return for the firm:

{eq}Annual \ realized \ return \ = \ \left ( \left ( 1 \ + \ Return_{Q_2} \right ) \ \times \ \left ( 1 \ + \ Return_{Q_3} \right ) \ \times \ \left ( 1 \ + \ Return_{Q_4} \right ) \ \times \ \left ( 1 \ + \ Return_{Q_5} \right ) \right ) \ - \ 1 \\ Annual \ realized \ return \ = \ \left ( \left ( 1 \ + \ 0.0667 \right ) \ \times \ \left ( 1 \ + \ 0.2333 \right ) \ \times \ \left ( 1 \ + \ 0.0000 \right ) \ \times \ \left ( 1 \ - \ 0.1818 \right ) \right ) \ - \ 1 \\ Annual \ realized \ return \ = \ \left ( \left ( 1.0667 \right ) \ \times \ \left ( 1.2333 \right ) \ \times \ \left ( 1.0000 \right ) \ \times \ \left ( 0.8182 \right ) \right ) \ - \ 1 \\ Annual \ realized \ return \ = \ 1.0764 \ - \ 1 \\ Annual \ realized \ return \ = \ 0.0764 \ or \ 7.6\% {/eq}

Hence option b is correct.