Final answer:
To determine the price per share of Babble, Inc., calculate the present value of the expected future profits and divide by the number of shares. Using a 15% discount rate, the total present value of the future profits is $51.3 million, leading to a price of $256,500 per share.
Step-by-step explanation:
To calculate the price an investor would be willing to pay for a share of stock in Babble, Inc., we need to consider the present value (PV) of the expected dividends, which are the company's future profits. The firm plans to disband in two years, and the profits are expected to be distributed at the time they are earned. We will use a discount rate of 15% to compute the present value of the future dividends.
First, the present value of the immediate $15 million profit is $15 million because it is already in the present value. The formula for the present value of a future sum of money is PV = Future Value / (1 + r)^n where r is the interest rate and n is the number of periods.
Next, calculate the present value of the profits expected one year and two years from now. The PV for the $20 million at year one is $20 million / (1 + 0.15)^1, and the PV for the $25 million at year two is $25 million / (1 + 0.15)^2.
After computing the PV for each of these profits, we add them together to find the total present value of the company's future profits. Finally, divide this total by the number of shares to determine the price per share. Given 200 shares, the calculation is as follows:
- $15 million / 1 = $15 million (Immediate profit, already in present value)
- $20 million / (1 + 0.15)^1 = $17.39 million (One year from now)
- $25 million / (1 + 0.15)^2 = $18.91 million (Two years from now)
The total present value of the future profits is then $15 million + $17.39 million + $18.91 million = $51.3 million. Dividing this by the number of shares we get, $51.3 million / 200 = $256,500 per share.