Question

An investor purchases 198 shares of XYZ. At the end of years 1,2 , and 3 the share price is 0.5,0.7, and 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

The investor reinvests dividends to purchase additional shares of XYZ at the end of each year for three years, resulting in a total ownership of 271.81 shares at the end of year three.

Step-by-step explanation:

To determine how many shares the investor owns at the end of three years when dividends are reinvested to purchase additional shares, we must calculate the additional shares purchased at each year's end and sum them with the initial 198 shares.

At the end of year 1, the dividend is $0.06 per share. The investor receives 198 × $0.06 = $11.88 in dividends and can buy $11.88 / $0.5 = 23.76 additional shares. At the end of year 2, the dividend is $0.08 per share, and the total number of shares is now 198 + 23.76 = 221.76. The dividends will be 221.76 × $0.08 = $17.74, which allows the purchase of $17.74 / $0.7 = 25.34 additional shares. Finally, at the end of year 3, the dividend is $0.10 per share, and the investor has 221.76 + 25.34 = 247.10 shares. The dividend yields 247.10 × $0.10 = $24.71, purchasing $24.71 / $1 = 24.71 more shares.

The total number of shares the investor owns at the end of year 3 is 198 + 23.76 + 25.34 + 24.71 = 271.81 shares to two decimal points.