Question

Rachel paid \(\$ 10\) per share for 100 shares of common stock in her favorite clothing store. a. If she receives 10 cents per share in dividends each year, about how many years would it take her to earn \(\$ 100\) on her investment? b. If the share price increases to \(\$ 11\) in two years and she chooses to sell the stock, how much capital gain would she make?

Short answer

a. 10 years; b. $100 capital gain.

Step-by-step solution

Understand the Dividend Earnings

Rachel receives 10 cents per share in dividends annually. Since she owns 100 shares, her annual dividend earnings are \(0.10 \times 100 = \$10\) per year.

Calculate Years to Earn $100 on Dividends

To calculate how many years it will take Rachel to earn \\(100 from her dividends, divide \\)100 by her annual dividend earnings of \$10. This means \( \frac{100}{10} = 10 \) years.

Determine Initial Investment

Rachel paid \\(10 per share for 100 shares. Her total initial investment was \(10 \times 100 = \\)1000\).

Calculate New Investment Value

After two years, the share price increased to \\(11 per share. The new value of her investment is \(11 \times 100 = \\)1100\).

Compute Capital Gain

The capital gain is the difference between the new investment value and the initial investment. This is \(1100 - 1000 = \$100\).

Key concepts

Dividends Calculation

When you invest in stocks, you may receive a portion of the company’s profits called dividends. Dividends are payments made to shareholders, usually annually or quarterly, as a reward for investing in the company. They can be seen as a form of income from your investment.
For Rachel's example, she receives 10 cents per share each year. This amount might seem small for a single share, but it adds up if you own multiple shares. For 100 shares, it amounts to \(0.10 \times 100 = \\(10\) per year in dividends.

• To reach \\)100 from dividends, Rachel would need her money to earn 10 times her annual dividend income, which takes \(\frac{100}{10} = 10\) years.

It’s essential to understand such calculations, as they give insight into the additional income you can gain from your investment aside from the increase in stock price.

Capital Gains

Capital gains refer to the profit earned when you sell stocks for more than you paid for them. It is the difference between the selling price and the purchase price. This is considered another form of return on your investment besides dividends.
In Rachel's case, she bought her shares for \(\\(10\) each, investing a total of \(\\)1000\). After two years, each share is worth \(\\(11\). When multiplied by 100 shares, this equates to \(11 \times 100 = \\)1100\) in total investment worth.

• The capital gain Rachel makes when selling her stocks at \\(11 each is calculated as the difference: \(1100 - 1000 = \\)100\). This means she made an extra \$100 from just holding and selling the stock.

Capital gains can be an important factor for investors as they contribute to the total return on investment. They rely on the ability to sell at a higher price than the purchase price.

Investment Returns

Investment returns encompass all the income from a particular investment, including both dividends and capital gains. Understanding this is crucial for evaluating the total effectiveness and potential of an investment.
Rachel's total investment returns consist of her cumulative dividends received over time and her capital gain. For Rachel:

• She earns \\(10 annually from dividends. Over ten years, this sums to \\)100.
• From selling her shares after two years at the increased price, she gains an additional \\(100 in capital gains.
• Therefore, her total returns are \\)200.

Investors should consider both these components to evaluate their investment's performance. Returns from dividends provide steady income, while capital gains can offer significant profit opportunities, especially when the market value of shares increases over time.