b) 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 R&D division generates two new product proposals every three years, so that there is a 66% chance that a project will be proposed every year. Typically, the investment opportunities the R&D division produces require an initial investment of 10 million and yield profits of 1 million per year that grow at one of three possible growth rates in perpetuity: 3%, 0%, and 3%. 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 the cost of capital will always remain at 12% per year. What is the present value of all future growth opportunities Big Industries will produce?

[15 marks]