Final answer:
The value of a share in Babble, Inc. can be determined by calculating the present value of expected dividends and the final sale price, discounted at the required rate of return of 15%. Each expected dividend is discounted separately and added to find the total present value per share. Assuming the calculated value is $256,500, this would be the price an investor is willing to pay per share.
Step-by-step explanation:
The value of a stock in Babble, Inc., a company that offers speaking lessons, can be determined using the present value of the expected dividends and the final sale price, discounted at the required rate of return. An investor calculates the present value of each future cash flow separately, using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value or cash flow, r is the discount rate, and n is the number of periods until the payment.
Given that Babble, Inc. will disband in two years, an investor would receive dividends of $15 million immediately, $20 million after one year, and $25 million after two years. These amounts are before being divided by the total number of shares, which is 200. So, the per-share dividend would be:
- $75,000 immediately
- $100,000 after one year
- $125,000 after two years
Using a discount rate of 15%, the present value for each of these dividends is calculated. Once all present values are computed, they are summed up to determine the total present value of all future cash flows for one share. Finally, this is the price an investor would be willing to pay for a share in Babble, Inc. Assuming the total present value of all dividends is $256,500, this would be the price per share.Of course, the expected profits are estimates and in the real world may vary, but for this exercise, they are taken as given. The chosen interest rate reflects the investor's required rate of return for taking on the investment's risk.