a company paid dividend of $7 per share and has announced that it will increase the dividend by $4 per share each of the next 4 years and then never pay another dividend again. the required rate of return is 11 percent on the company's stock. How much will you pay today?
To calculate how much you should pay today for the stock, you need to estimate the present value of the future cash flows, which in this case are the dividends. Here's how you can calculate it:
1. Determine the future dividends:
The company is planning to increase the dividend by $4 per share each year for the next 4 years. So, the future dividends will be $7 (current dividend) + $4 (increase in dividend) for the first year, $7 + $4 + $4 for the second year, $7 + $4 + $4 + $4 for the third year, and $7 + $4 + $4 + $4 + $4 for the fourth year.
Therefore, the future dividends will be: $7, $15, $19, $23, and $23 for the first to fourth years respectively.
2. Calculate the present value of future dividends:
To calculate the present value of future cash flows, we need to discount each year's dividends to their present value using the required rate of return, which is 11 percent in this case. The formula for present value is:
Present Value = Future Cash Flow / (1 + Required Rate of Return)^(Number of Periods)
For each year's dividend, divide it by (1 + 0.11) raised to the power of the number of years in the future.
Present Value of Year 1 Dividend = $7 / (1 + 0.11)^1
Present Value of Year 2 Dividend = $15 / (1 + 0.11)^2
Present Value of Year 3 Dividend = $19 / (1 + 0.11)^3
Present Value of Year 4 Dividend = $23 / (1 + 0.11)^4
Present Value of Year 5 Dividend = $23 / (1 + 0.11)^5
3. Calculate the total present value of future dividends:
Add up all the present values of dividends to get the total present value.
Total Present Value = Present Value of Year 1 Dividend + Present Value of Year 2 Dividend + Present Value of Year 3 Dividend + Present Value of Year 4 Dividend + Present Value of Year 5 Dividend
Finally, the amount you should pay today for the stock is equal to the total present value of future dividends.