Final answer:
To calculate the value an investor will pay for a share of stock in Babble, Inc., we use the dividend discount model (DDM) to find the present value of future dividends. The dividends expected over the next two years are discounted at a required rate of return to get their present values. Adding up the present values gives the value of a share of stock in the company.
Step-by-step explanation:
To calculate the value an investor will pay for a share of stock in Babble, Inc., we need to use the dividend discount model (DDM). The DDM is based on the concept that the value of a stock is the present value of all its future dividends. In this case, the dividends are expected to be $15 million, $20 million, and $25 million in the present, one year from now, and two years from now respectively. Using a required rate of return, the future dividends can be discounted to their present value.
Let's assume a required rate of return of 10%. Using this rate and the formula for the present value of a future cash flow, we can calculate the present value of each dividend:
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- Present Value of $15 million in the present = $15 million / (1 + 0.10)^0 = $15 million
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- Present Value of $20 million in one year = $20 million / (1 + 0.10)^1 = $18.18 million
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- Present Value of $25 million in two years = $25 million / (1 + 0.10)^2 = $20.66 million
The value of a share of stock in Babble, Inc. would be the sum of the present values of all the future dividends:
Total value = $15 million + $18.18 million + $20.66 million = $53.84 million