Peterson Paving is planning to bid on a highway project for the new twinning. The start$-$up costs would be $$1,000,000,$ which includes purchasing equipment, licensing, etc. Assume Peterson expects an annual return on investment of $7\%.$ The company$$s research shows annual incomes and annual expenses in thousands of dollars $($$$1000$s$)$ for the next four $(4)$ years of:

Year $1234$ Revenue $4006008001000$ Expenses $500400300200$

$($a$)$ What is the NPV of this project for these five years $($including year $0)?$

$($b$)$ Should Peterson Paving bid on this project? Why or why not?

$($c$)$ Which of the following describes the internal rate of return $($IRR$)$ for this project? $($i$)$ IRR $<7\%($ii$)$ IRR $=7\%($iii$)$ IRR $>7\%$

Justify your choice.