Final answer:
To calculate the price an investor will pay for a share of stock in Babble, Inc., we need to find the present value of the future dividend payments. Using an assumed interest rate of 15%, we can calculate the present value of each dividend payment and then add them up to get the total present value of the dividend stream. Dividing this total by the number of shares gives us the price per share.
Step-by-step explanation:
To calculate what an investor will pay for a share of stock in Babble, Inc., we need to find the present value of the future dividend payments. We can use the concept of present value to discount the future dividends back to their present value. In this case, we assume a 15% interest rate. The present value of each dividend can be calculated using the formula: PV = FV / (1 + r)t, where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years in the future. After finding the present value of each dividend, we add them up to get the total present value of the dividend stream. Finally, we divide this total by the number of shares to find the price per share.
In this case, the present value of the three dividend payments would be: $2.85 / (1 + 0.15)1 + $4.12 / (1 + 0.15)2 + $3.75 / (1 + 0.15)3. After calculating these values, we can add them up to get the present value of the dividend stream. If the total present value of the dividend stream is $51.3 million and there are 200 shares, then the price per share would be about $256,500 per share.
It's important to note that these calculations are based on assumptions and the interest rate used may vary depending on the risk and other factors in the market.