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:

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 year

Unit 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.$)$