Problem
You are an analyst working for Goldman Sachs, and you are trying to value the growth potential of a large, established company, Big Industries. Big Industries has a thriving R&D division that has consistently turned out successful products. You estimate that, on average, the division launches two projects every three years, so you estimate that there is a 60% chance that a project will be produced every year. Typically, the investment opportunities the R&D division produces require an initial investment of $9.8 million and yield profits of $1.07 million per year that grow at one of three possible growth rates in perpetuity: 2.5%, 0.0%, and - 2.5%. All three growth rates are equally likely for any given project. These opportunities are always "take it or leave it" opportunities: If they are not undertaken immediately, they disappear forever. Assume that all the probabilities are risk-neutral probabilities, which means the cost of capital is always the risk-free rate and risk-free rates follow this path: The current interest rate for a risk-free perpetuity is 7.7%; in one year, there is a 65% chance that all risk-free interest rates will be 9.9% and stay there forever and a 35% chance that they will be 5.9% and stay there forever. The current one-year risk-free rate is 7.1%.
• What is the present value of all future growth opportunities Big Industries will produce? (Hint: Make sure to round all intermediate calculations to at least four decimal places.) .
• What is the present value at time 0 of all future growth opportunities?