P$3(5$ points$)$ Terrific Toys, a large profitable producer of toys and games, is considering the introduction of a new toy called Gooey Guck that it hopes will be a new fad. It is likely to be popular for three years, but after that, consumers will tire of the new toy. It forecasts that it can sell $3$ million units next year and $2$ million units in the second year, and $1$ million units in the third year.Machinery must be purchased immediately at a cost of $$15$ million $($which can be depreciated for tax purposes straight$-$line over three years$).$ After three years the machinery will be disposed and there will be no salvage value.The cost of manufacturing Gooey Guck will be $$2\mathrm{.}5$ per unit $($primarily labour and raw materials$),$ and they hope to sell it for $$6$ per unit.The corporate tax rate is $20\%.$ There is no inflation. The appropriate discount rate is $10\%.$What is the NPV of introducing Gooey Guck? Should they make the investment? Show all your work.