You buy a stock for $1000 and expect to sell it for $900 after four years but also expect to collect dividends of $120 a year. Prove that the return on this investment is less than 10%?
To calculate the return on an investment, we need to consider both the capital gains (or losses) and the dividends received over the holding period. In this case, we have the initial investment of $1000, an expected selling price of $900, and annual dividends of $120.
First, let's calculate the total dividends received over the four-year period. Since we receive $120 annually, the total dividends can be calculated as follows:
Total dividends = Annual dividends * Number of years
Total dividends = $120 * 4
Total dividends = $480
Now, let's calculate the capital gain or loss. We initially bought the stock for $1000 and expect to sell it for $900 after four years. Therefore, the capital loss can be calculated as:
Capital loss = Initial investment - Expected selling price
Capital loss = $1000 - $900
Capital loss = $100
To determine the return on investment (ROI), we need to find the total gain or loss. The total gain or loss can be calculated by adding the capital gain or loss to the total dividends received:
Total gain or loss = Capital gain or loss + Total dividends
Total gain or loss = -$100 + $480
Total gain or loss = $380
Finally, let's calculate the ROI using the formula:
ROI = (Total gain or loss / Initial investment) * 100
ROI = ($380 / $1000) * 100
ROI = 38%
The return on investment is 38%, which is higher than 10%. Therefore, the statement that the return on this investment is less than 10% is false.