Final answer:
An investor would be willing to pay approximately $269,200 per share of Babble Inc., assuming a required rate of return of 10% and the present value of future dividends is the primary method of valuation given that the company will be disbanded in two years.
Step-by-step explanation:
Valuing Shares of Babble, Inc.
To determine the price an investor would pay for a share of Babble, Inc., one needs to consider the present value of the future dividends since the company will be disbanded in two years. The present value of the dividends can be calculated using the formula for the present value of annuities:
Present Value (PV) = C / (1+r)^t, where C is the cash dividend, r is the discount rate (expected rate of return), and t is the time period.
Assuming an investor would require a 10% rate of return (just as an example), you would calculate the present value (PV) of each dividend and sum them to get the total value of all dividends. This total value would be divided by the number of shares to determine the price per share:
Present value of the $15 million dividend paid immediately: $15 million / (1+0.10)^0 = $15 million
Present value of the $20 million dividend in one year: $20 million / (1+0.10)^1 = $18.18 million
Present value of the $25 million dividend in two years: $25 million / (1+0.10)^2 = $20.66 million
Adding these up gives a total present value of $53.84 million. Divided by the 200 outstanding shares, the price per share would be $269,200. Therefore, an investor would be willing to pay approximately $269,200 per share of Babble, Inc.