Final answer:
An investor would theoretically pay $1,452.67 for a share of stock in Babble, Inc., based on the present value of expected dividends, discounted at 3%, over the remaining life of the company.
Step-by-step explanation:
Determining the Value of Stock in Babble, Inc.
To determine what an investor would pay for a share of stock in Babble, Inc., we need to calculate the present value of the expected dividend payouts. Since the company will disband in two years, the investor will receive dividends just for these two years. The profits, which will be paid as dividends, are expected to be $15 million immediately, $20 million one year from now, and $25 million two years from now.
The number of shares is 200, so the dividends per share will be $75,000 immediately ($15 million / 200 shares), $100,000 in one year ($20 million / 200 shares), and $125,000 in two years ($25 million / 200 shares).
To calculate the present value of these dividends, we need to discount them back to their present value using the appropriate discount rate. If the risk-free rate is assumed to be the discount rate, which is common for a risk-free cash flow, we would use 3% as given in the question.
Calculating the present value (PV) for each dividend:
- PV of immediate dividend = $75,000
- PV of year-one dividend = $100,000 / (1 + 0.03) = $97,087.38
- PV of year-two dividend = $125,000 / (1 + 0.03)^2 = $118,446.60
The total present value of these dividends is the sum of the individual present values: $75,000 + $97,087.38 + $118,446.60 = $290,534.
Therefore, the fair price an investor might pay for a share of stock in Babble, Inc. would be $290,534 / 200 shares = $1,452.67