The process for producing integrated circuits for computer motherboards has an initial cost of $$500,000($investment at year $0),$ with annual costs of $$80,000$ and revenues of $$270,000$ per year starting $5$ years from now. In year $6,$ $$25000$ was given to the company by the Environmental Protection Agency as credit for its environmental compliance. What is the payback period at

a$)0\%$

b$)8\%$

Given the two guesses for Payback Period to be between $4$yrs and $5$ yrs at $8\%$ from the $5^{th}$ year they started having expenses and revenue.