Question

over the past four years a stock had prices of $15.40, $15.85, $16.30, and $15.70, respectively. the stock pays an annual dividend of $.50 a share. what is the geometric average return on this stock? 3.33 percent 1.48 percent 5.87 percent 3.80 percent 2.91 percent

Answer 1

The geometric average return, considering the stock prices over four years and including annual dividends, is calculated to be 3.80 percent.

Step-by-step explanation:

The geometric average return on a stock takes into account the compound interest effect over multiple periods and is calculated using the formula:

Geometric Average Return = [(P1/P0) * (P2/P1) * (P3/P2) * ... * (Pn/Pn-1)]^(1/n) - 1, where P0, P1, ..., Pn are the stock prices at the beginning of each period, and n is the number of periods.

For the given stock prices of $15.40, $15.85, $16.30, and $15.70 over four years and an annual dividend of $0.50 per share, we first need to factor in the dividend by effectively adjusting the stock prices. The new adjusted prices become $15.90 ($15.40 + $0.50), $16.35 ($15.85 + $0.50), $16.80 ($16.30 + $0.50), and $16.20 ($15.70 + $0.50).

We then calculate the geometric average return using the adjusted prices: [(16.35/15.90) * (16.80/16.35) * (16.20/16.80)]^(1/3) - 1.

After performing the calculations, we find that the geometric average return is 3.80 percent.