Question

An investor purchases 189 shares of XYZ. At the end of years 1,2 , and 3 the share price is 0.6,0.8, and 1.1 dollars, respectively. At the end of years 1,2 , and 3 the company issues dividends of $0.06,$0.08, and $0.10, respectively. The investor elects to use the dividends she receives to purchase additional shares. How many shares does she own at the end of three years to two decimal points of accuracy?

Answer 1

After reinvesting dividends for three years, the investor will own a total of 249.48 shares of XYZ company.

To calculate the total number of shares an investor owns at the end of three years when using dividends to purchase additional shares, we need to take into account the share price and the dividends issued at the end of each year.

Initially, the investor has 189 shares. At the end of year 1, with a dividend of $0.06 per share, the investor receives 189 shares * $0.06/share = $11.34 in dividends. With the share price at $0.6, this allows the investor to buy $11.34 / $0.6 = 18.9 additional shares. New total = 189 + 18.9 = 207.9 shares.

At the end of year 2, the new dividend is $0.08 per share. Now, the investor receives 207.9 shares * $0.08/share = $16.632 in dividends. With the share price at $0.8, they can purchase $16.632 / $0.8 = 20.79 additional shares. New total = 207.9 + 20.79 = 228.69 shares.

In year 3, the dividend is $0.10 per share. The investor gets 228.69 shares * $0.10/share = $22.869 in dividends. With the share price at $1.1, it allows them to buy $22.869 / $1.1 = 20.79 additional shares. Final total = 228.69 + 20.79 = 249.48 shares.

The investor owns 249.48 shares at the end of three years, assuming they reinvest all dividends into purchasing additional shares.