Final answer:
To calculate the current value of a share in a company with varying annual dividend growth rates, calculate the present value of expected dividends using the required rate of return, and divide by the number of shares. In the case of Babble, Inc., an investor would pay around $256,500 per share based on expected payouts and a 15% interest rate.
Step-by-step explanation:
The value of a share in a company that plans to increase its annual dividend by a certain percentage for a number of years, and then decrease it afterward, can be calculated using the present value of these dividends adjusted for the required rate of return.
To determine what an investor would pay for a share of Babble, Inc., one would calculate the present value (PDV) of the expected dividends. This requires discounting the future dividends by the investor's required rate of return. Given the specific profits expected from Babble, Inc., and using the provided interest rate, the PDV of each year’s dividends is calculated and then added together. The total PDV is then divided by the number of shares to determine the price per share.
If Babble, Inc. expects to pay out $15 million immediately, $20 million one year from now, and $25 million two years from now, and there are 200 shares of stock, the present value of the future profits would be calculated for each time period using the 15% interest rate, totaled, and then divided by the number of shares to find the price per share. This results in a price of approximately $256,500 per share.