Final answer:
To determine the value of a share of Babble, Inc., future profits are discounted to present value using a 15% interest rate, summed up, and divided by the number of shares. The final valuation of a share is approximately $256,600.
Step-by-step explanation:
To calculate what an investor would pay for a share of stock in Babble, Inc., we need to discount the expected future profits to their present value (PV) using the given interest rate of 15% and then divide by the number of shares. The present value of the profits can be calculated for each year:
- Present Value Year 0 (immediate): $15 million / (1 + 0.15)^0 = $15 million
- Present Value Year 1: $20 million / (1 + 0.15)^1 = $17.39 million
- Present Value Year 2: $25 million / (1 + 0.15)^2 = $18.93 million
Next, add up all the present values for the different time periods: $15 million + $17.39 million + $18.93 million = $51.32 million. The PV of total profits divided by the number of shares (200) gives us the price per share: $51.32 million / 200 = $256,600. Thus, each share of stock should be valued at approximately $256,600 per share.