Final answer:
The value of a share of stock in Babble, Inc. can be found by calculating the present value of anticipated future dividend payouts. Due to the lack of a discount rate, a numerical answer cannot be specified. For illustrative purposes, with an assumed discount rate of 15%, a share would be valued at approximately $256,500.
Step-by-step explanation:
The student's question is related to valuing a share of stock given a certain dividend growth scenario. To determine the value of a share of stock in Babble, Inc., we need to consider the present value of future dividends since all profits are paid out as dividends. We must calculate the present value of each dividend payment and sum them up. With an anticipated growth rate of 7 percent in dividends and a current dividend of $2.75 per share, if the stock is selling for $49.1 per share, we can use the Gordon Growth Model to find the required rate of return. However, as we have specific future dividend payments for Babble, Inc., we just discount them back to their present value.
The present value (PV) calculations are based on a specific interest rate, which is not provided in the student's question nor in the Babble, Inc. example. To calculate the PV of a future amount, we use the formula PV = FV / (1 + r)^n, where FV is the future value of the dividend, r is the discount rate, and n is the number of periods until the payment. In our example, we would do this for the $15 million immediate dividend, the $20 million one year from now, and the $25 million two years from now, then divide by the total number of shares.
We can understand that the price per share of Babble, Inc. would be the sum of these present values divided by the number of shares. As an illustrative example, if we assumed a discount rate of 15%, the total present value of profits would be $51.3 million; dividing by 200 shares gives us $256,500 per share.