The Trid Soap Company is developing a radically new soap powder that is expected to take $3$ years to develop and cost approximately $$6$ million per year. At the end of the $3$ years, Trid will know if the product is a technical success; at the present time, Trid managers estimate that there is an $80\%$ likelihood that they will be successful in developing the soap powder. Assuming the R&D succeeds, Trid can launch the product in Year $4$ at an estimated cost of $$5\mathrm{.}5$ million. If launched, the marketing VP $($Vice President$)$ estimates that the new product would be a commercial success with probability $0\mathrm{.}6$; if it is commercially successful, it would earn gross revenues of $$15$ million per year for $5$ years. If not a commercial success, the new soap powder would only earn an estimated $$2$ million per year. Assuming an annual discount rate of $12\%,$ what is the NPV of this project? Would you recommend that Trid proceed with this project?