Perot Corporation is developing a new CPU chip based on a new type of technology. Its new chip, the Patay$2$ chip, will take two years to develop. However, because other chip manufacturers will be able to copy the technology, it will have a market life of two years after it is introduced. Perot expects to be able to price the chip higher in the first year, and it anticipates a significant production cost reduction after the first year as well. The relevant information for developing and selling the Patay$2$ is given as follows:

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PATAY$2$ CHIP PRODUCT ESTIMATES$$Development cost$$20,000,000$Pilot testing$$5,000,000$Debug$$3,700,000$Ramp$-$up cost$$3,000,000$Advance marketing$$6,400,000$Marketing and support cost$$1,000,000$per yearUnit production cost year $1$$$655\mathrm{.}00$Unit production cost year $2$$$545\mathrm{.}00$Unit price year $1$$$820\mathrm{.}00$Unit price year $2$$$650\mathrm{.}00$Sales and production volume year $1250,000$Sales and production volume year $2150,000$Interest rate$10\%$

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Assume all cash flows occur at the end of each period.

a$.$ What is the net present value $($at the discount rate of $10\%)$ of this project? $($Negative value should be indicated by a minus sign. Enter your answer in thousands of dollars. Round your answer to the nearest thousand.$)$

b$.$ Perot$$s engineers have determined that spending $$10$ million more on development will allow them to add even more advanced features. Having a more advanced chip will allow them to price the chip $$50$ higher in both years $($$$870$ for year $1$ and $$700$ for year $2).$ What is the NPV of the project if this option is implemented? $($Negative value should be indicated by a minus sign. Enter your answer in thousands of dollars. Round your answer to the nearest thousand.$)$

c$.$ If sales are only $200,000$ the first year and $100,000$ the second year, what would the NPV of the project be$?$ Assume the development costs and sales price are as originally estimated. $($Negative value should be indicated by a minus sign. Enter your answer in thousands of dollars. Round your answer to the nearest thousand.$)$