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 $68\%$ chance that a project will be produced every year. Typically, the investment opportunities the R&D division produces require an initial investment of $$9\mathrm{.}6$ million and yield profits of $$0\mathrm{.}95$ million per year that grow at one of three possible growth rates in perpetuity: $2\mathrm{.}9\%,0\mathrm{.}0\%,$ and $-2\mathrm{.}9\%.$ 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 $8\mathrm{.}1\%$; in one year, there is a $63\%$ chance that all risk$-$free interest rates will be $10\mathrm{.}1\%$ and stay there forever and a $37\%$ chance that they will be $6\mathrm{.}4\%$ and stay there forever. The current one$-$year risk$-$free rate is $6\mathrm{.}6\%.$ What is the present value of all future growth opportunities Big Industries will produce?