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 $69\%$ chance that a project will be

produced every year. Typically, the investment opportunities the R&D division produces require an initial investment of $$9\mathrm{.}9$ million and yield profits of $$1\mathrm{.}06$ 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 $7\mathrm{.}7\%$; in one year, there is a $61\%$ chance that all risk$-$free interest rates will be $9\mathrm{.}7\%$ and stay there forever and a $39\%$ chance that they

will be $5\mathrm{.}7\%$ and stay there forever. The current one$-$year risk$-$free rate is $7\mathrm{.}2\%.$ 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.$)$ PLEASEEE!