Final answer:
To calculate the price per share for Babble, Inc., you sum the present values of the expected profits paid as dividends immediately, in one year, and two years from now, and divide by the number of shares. If the discount rate is 10%, the price per share is the sum of the present values of $15 million, $20 million, and $25 million, divided by the number of shares (200).
Step-by-step explanation:
The question is asking us to calculate the present value of the future dividends to determine the current share price for Babble, Inc. To determine what an investor would be willing to pay for a share of stock in Babble, Inc., we use the present value formula for expected dividends. The company expects profits of $15 million immediately (present value is simply $15 million), $20 million one year from now, and $25 million two years from now. Assuming an appropriate discount rate (let's say 'r'), the present value (PV) of these dividends can be calculated by summing the present values of all future dividends. The PV for the year one dividend is $20 million / (1 + r), and for year two dividend, it's $25 million / (1 + r)^2. Summing these up and dividing by the number of shares (200) will give us the price per share.
For example, if the discount rate is 10% (0.1), the calculations would be:
- Immediate Dividend: PV = $15 million / 200 shares = $75,000 per share
- Year 1 Dividend: PV = $20 million / ((1 + 0.1) * 200 shares) = $90,909.09 per share
- Year 2 Dividend: PV = $25 million / ((1 + 0.1)^2 * 200 shares) = $103,305.79 per share
Add these up to get the total present value per share.