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.


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