$7.$ You are the CFO of a drug company, and you must decide whether to invest $15$M dollars in R&D for a new drug. If you conduct the R&D$,$ you believe that there is a $10\%$ chance that the research will produce a useful drug. If the research is successful, investment in the drug will require an outlay of $400$ million dollars. The drug will likely generate annual profits of $90$ million for $10$ years $($starting a year after the $400$ million dollar outlay$).$ After that, it will generate a cash flow equal to $7$ million a year in perpetuity $($no growth$).$ The discount rate is $10\%.$