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 $itis$ introduced. Perot expects $tobe$ 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$2is$ given $as$ follows:

PATAY$2$ CHIP PRODUCT ESTIMATES

Development cost: $ $20,000,000$

Pilot testing: $5,000,000$

Debug: $ $2,800,000$

Ramp$-upcost$: $3,000,000$

Advance marketing: $4,600,000$

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 $1$: $820.00$

Unit price year $2$: $650.00$

Sales and production volume year $1$: $250,000$

Sales and production voume year $2$: $150,000$

Interest rate: $10\%$

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

$a.$ What $is$ the net present value $(at$ the discount rate $of10\%)of$ 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 $NPVof$ 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 $NPVof$ 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.$)$